Papers by Jonathan D. H. Smith

1975-80 / 1981-85 / 1986-88 / 1989 / 1990-91 / 1992-93 / 1994-95 / 1996 / 1997-99 / 2000 / 2001 / 2002 / 2003 / 2004 / 2005 / 2006 / 2007 / 2008 / 2009 / 2010 / 2011 / 2012 / 2013 / 2014 / 2015 / 2016 / 2017 / 2018 / 2019 / 2020 / 2021 / 2022 / 2023 / 2024 / to appear

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  1. Centraliser rings of multiplication groups on quasigroups, Math. Proc. Camb. Phil. Soc. 79 (1976), 427-431.
  2. Finite distributive quasigroups, Math. Proc. Camb. Phil. Soc. 80 (1976), 37-41.
  3. On the nilpotence class of commutative Moufang loops, Math. Proc. Camb. Phil. Soc. 84 (1978), 387-404.
  4. A second grammar of associators, Math. Proc. Camb. Phil. Soc. 84 (1978), 405-415.
  5. (with G. Czédli) On the uniqueness of Mal'cev polynomials, in Colloq. Math. Soc. János Bolyai 28. "Finite Algebra and Multiple-valued Logic'', Szeged, 1979.
  6. Finite equationally complete entropic quasigroups, pp. 345--356 in "Contributions to General Algebra'' (H. Kautschitsch, W. B. Müller, W. Nöbauer, eds.), Johannes Heyn, Klagenfurt, 1979.
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  7. Exterior algebra representations of commutative Moufang loops, Arch. Math. 34 (1980), 393-398.
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  8. In defence of eponymy, Math. Intelligencer 3 (1981), 89-90.
  9. (with A.B. Romanowska) Bisemilattices of subsemilattices, J. Algebra 70 (1981), 78-88.
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  10. Commutative Moufang loops and Bessel functions, Inv. Math. 67 (1982), 173-187.
    Available online.
  11. (with K.W. Johnson) Characters of finite quasigroups, Eur. J. Comb. 5 (1984), 43-50.
    Available online.
  12. Two enumeration principles for free algebras, Acta Univ. Carolinae (Math. et Phys.) 25 (1984), 53-58.
    Available online.
  13. (with A.B. Romanowska) Distributive lattices, generalizations, and related non-associative algebras, Houston J. Math. 11 (1985), 367-383.
  14. (with A.B. Romanowska) From affine to projective geometry via convexity, pp. 255-269 in "Universal Algebra and Lattice Theory'' (ed. S. D. Comer), Springer Lecture Notes in Mathematics, Berlin, 1985.
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  15. Commutative Moufang Loops: the first 50 years, Algebras, Groups and Geometries 2 (1985), 209-234.
  16. (with K.W. Johnson) Characters of finite quasigroups II: induced characters, Eur. J. Comb. 7 (1986), 131-137.
    Available online.
  17. (with K.W. Johnson) A note on character induction in association schemes, Eur. J. Comb. 7 (1986), 139.
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  18. Modal theory, partial orders, and digital geometry, in "The Mathematical Foundations of Programming Semantics'' (A. Melton, ed.), Springer Lecture Notes in Computer Science, Berlin, 1986.
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  19. Minimal trees of given search number, Discrete Math. 66 (1987), 191-202.
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  20. Multilinear algebras and Lie's theorem for formal n-loops, Arch. Math. 51 (1988), 169-177.
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  21. Quasigroups, association schemes, and Laplace operators on almost periodic functions, pp. 205-218 in "Algebraic, Extremal and Metric Combinatorics 1986'' (M.-M. Deza, P. Frankl and I.G. Rosenberg, eds.), Cambridge University Press, Cambridge, 1988.
  22. (with K.W. Johnson) Characters of finite quasigroups III: quotients and fusion, Eur. J. Comb. 10 (1989), 47-56.
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  23. (with A.B. Romanowska) Subalgebra systems of idempotent entropic algebras, J. Algebra 120 (1989), 247-262.
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  24. (with A.B. Romanowska) On the structure of subalgebra systems of idempotent entropic algebras, J. Algebra 120 (1989), 263-283.
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  25. (with K.W. Johnson) Characters of finite quasigroups IV: products and superschemes, Eur. J. Comb. 10 (1989), 257-263.
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  26. Induced class functions are conditional expectations, Eur. J. Comb. 10 (1989), 293-296.
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  27. (with A.B. Romanowska) Support functions and ordinal products, Geom. Dedicata 30 (1989), 281-296.
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  28. (with D.R. Brooks et al.) Entropy and information in evolving biological systems, Biology and Philosophy 4 (1989), 407-432.
  29. (with K.W. Johnson) Characters of finite quasigroups V: linear characters, Eur. J. Comb. 10 (1989), 449-456.
    Available online.
  30. (with A.B. Romanowska) On the structure of barycentric algebras, Houston J. Math. 16 (1990), 431-448.
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  31. Entropy, character theory and centrality of finite quasigroups, Math. Proc. Camb. Phil. Soc. 108 (1990), 435-443.
  32. (with K.W. Johnson and S.Y. Song) Characters of finite quasigroups VI: critical examples and doubletons, Eur. J. Comb. 11 (1990), 267-275.
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  33. (with A.B. Romanowska) Communicating processes and entropic algebras, Fund. Informaticae 13 (1990), 263-274.
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  34. Combinatorial characters of quasigroups, pp. 163-187 in "Coding Theory and Design Theory, Part I: Coding Theory'' (ed. D. Ray-Chaudhuri), Springer, New York, NY, 1990.
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  35. (with A.B. Romanowska) Differential groupoids, pp. 283-290 in "Contributions to General Algebra 7" (D. Dorninger, G. Eigenthaler, H.K. Kaiser and W.B. Müller, eds.), Hölder-Pichler-Tempsky, Vienna, 1991.
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  36. Finite codes and groupoid words, Eur. J. Comb. 12 (1991), 331-339.
  37. Skein polynomials and entropic right quasigroups, Demonstr. Math. 24 (1991), 241-246.
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  38. (with A.B. Romanowska) On the structure of semilattice sums, Czech. J. Math. 41 (116) (1991), 24-43. Available online .
  39. (with J.D. Phillips) The endocenter and its applications to quasigroup representation theory, Comm. Math. Univ. Carol. 32 (1991), 417-422. Available online .
  40. (with X.R. Shen) Representation theory of comtrans algebras, J. Pure and Appl. Alg. 80 (1992), 177-195. Available online.
  41. Quasigroups and quandles, Discrete Math. 109 (1992), 277-282. Available online.
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  42. Loop transversals to linear codes, J. Comb., Info. and System Sciences 17 (1992), 1-8.
  43. (with X.R. Shen) Comtrans algebras and bilinear forms, Arch. Math. 59 (1992), 327-333.
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  44. (with X.R. Shen) Simple multilinear algebras, rectangular matrices and Lie algebras, J. Algebra 160 (1993), 424-433. Available online.
  45. (with A.B. Romanowska) Separable modes, Algebra Universalis 30 (1993), 61-71. Click here for local copy.
  46. Comtrans algebras and their physical applications, Banach Center Publications 28 (1993), 319-326.
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  47. Association schemes, superschemes, and relations invariant under permutation groups, Eur. J. Comb., 15 (1994), 285-291.
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  48. (with M.F. Hobart) Vector lattices and rooted trees, Algebra Universalis 34 (1995),110-117.
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  49. (with A. Dharwadker) Split extensions and representations of Moufang loops, Comm. Alg. 23 (1995), 4245-4255.
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  50. (with L. Thur) Subdifferentiation of monotone functions from semilattices to distributive lattices, Order 12 (1995), 307-313.
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  51. A left loop on the 15-sphere, J. Algebra 176 (1995), 128-138.
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  52. (with A. Pilitowska and A.B. Romanowska) Affine spaces and algebras of subalgebras, Algebra Universalis 34 (1995), 527-540.
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  53. (with M.A. Akivis et al.) Vladislav V. Goldberg, on the occasion of his 60th birthday and 35 years of scientific activity, Webs and Quasigroups, 1995, 5-10.
  54. (with X.R. Shen) Simple algebras of Hermitian operators, Arch. Math. 65 (1995), 534-539.
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  55. Competition and the canonical ensemble, Math. Biosci. 133 (1996), 69-83.
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  56. (with R. Rossmanith) Alternative approaches to alternative algebras, Acta Sci. Math. 62 (1996), 145-151.
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  57. (with T.S.R. Fuad) Quasigroups, right quasigroups, and category coverings, Algebra Universalis 35 (1996), 233-248.
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  58. (with A.A. Ungar) Abstract space-times and their Lorentz groups, J. Math. Phys. 37 (1996), 3073-3098. Available online.
  59. (with A.B. Romanowska) Semilattice-based dualities, Studia Logica 56 (1996), 225-261.
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  60. (with F.A. Hummer) Greedy loop transversal codes, metrics, and lexicodes, J. Comb. Math. Comb. Comp. 22 (1996), 143-155.
  61. (with F.-L. Hsu and F.A. Hummer) Logarithms, syndrome functions, and the information rates of greedy loop transversal codes, J. Comb. Math. Comb. Comp. 22 (1996), 33-49.
  62. (with A.B. Romanowska) Duality for semilattice representations, J. Pure Appl. Algebra, 115 (1997), 289-308.
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  63. Homotopy and semisymmetry of quasigroups, Algebra Universalis 38 (1997), 175-184. Available online.
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  64. Canonical ensembles, evolution of competing species, and the arrow of time, pp. 141-153 in "Evolutionary Systems: Biological and Epistemological Perspectives on Selection and Self-organization" (eds. G. van de Vijver, S.N. Salthe and M. Delpos), Kluwer, Dordrecht, 1998.
  65. Demography and the canonical ensemble, Math. Biosci. 153 (1998), 151-161.
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  66. (with J.D. Phillips) Quasiprimitivity and quasigroups, Bull. Australian Math. Soc. 59 (1999), 473-475.
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  67. Wreath products along the period-doubling route to chaos, Ergodic Th. and Dynamical Systems 19 (1999), 1617-1636.
  68. Modes and Modals, Discuss. Math. 19 (1999), 9-40.
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  69. Speed's orbit problem: variations on themes of Burnside, Eur. J. Comb. 20 (1999), 867-873. Available online.
  70. Quasigroup actions: Markov chains, pseudoinverses, and linear representations, Southeast Asia Bulletin of Mathematics 23 (1999), 719-729 (invited paper).
  71. On the evolution of semiotic capacity, pp. 283-309 in "Semiotics, Evolution, Energy" (ed. E. Taborsky), Shaker Verlag, Aachen, 1999.
  72. Classical and quantum statistical mechanics of permutation representations, pp. 337-348 in "Groups Korea '98, Proceedings of the International Conference, Pusan National University, Pusan, Korea, August 10-16, 1998" (eds. Y.G. Baik, D.L. Johnson, A.C. Kim), de Gruyter, Berlin, 2000.
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  73. (with M. Saniga) Plane cubic curves, three-webs and the dimensionality of space-time, Noetic J. 3 (2000), 1-20.
  74. A class of quasigroups solving a problem of ergodic theory, Comment. Math. Univ. Carol. 41 (2000), 409-414. Available online
  75. Loops and quasigroups: Aspects of current work and prospects for the future, Comment. Math. Univ. Carol. 41 (2000), 415-427. Available online
  76. (with T.S.R. Fuad et al.) Simple multilinear algebras and hermitian operators, Comment. Math. Univ. Carol. 41 (2000), 251-259. Available online
  77. Time in biological systems, pp. 75-96 in "Studies on the Structure of Time" (eds. R. Buccheri, V. di Gesù, M. Saniga), Kluwer, New York, NY, 2000.
  78. (with K.B. Athreya) Canonical distributions and phase transitions, Discuss. Math. Prob. and Stat. 20 (2000), 167-176.
    Online abstract.
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  79. (with M.A. Akivis et al.) V.V. Goldberg, On the occasion of his 65th birthday, Webs and Quasigroups, 2000, 7-13.
  80. Loop transversal codes, Cubo 3 (2001), 137-148 (invited expository paper). Click here for local copy.
  81. Some observations on the concepts of information-theoretic entropy and randomness, Entropy 3 (2001), pp. 1-11 (electronic journal).
  82. Information theory and its applications to biology, finance and physics (invited conference report), Entropy 3 (2001), pp. 64-65 (electronic journal).
  83. (with A.B. Romanowska) Embedding sums of cancellative modes into functorial sums of affine spaces, pp. 127-139 in "Unsolved Problems on Mathematics for the 21st Century - A Tribute to Kiyoshi Iséki's 80th Birthday" (eds. J. M. Abe and S. Tanaka), IOS Press, Amsterdam, 2001.
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  84. Quasigroup homogeneous spaces and linear representations, J. Algebra 241 (2001), 193-203. Available online.
  85. Regular orbits in powers of permutation representations, Arch. Math. 77 (2001), 138-142. Available online.
  86. (with X.R. Shen) Simple algebras of invariant operators, Alg. Colloq. 8 (2001), 285-291.
  87. Orbit decomposition of subset actions, Discrete Math. 247 (2002), 251-254. Available online.
  88. Three key questions about complex systems, Semiotics, Evolution, Energy, and Development 2 (2002) No.3, 13 pages (electronic journal).
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  89. (with J.Y. Choi) Tri-restricted numbers and powers of permutation representations, J. Comb. Math. Comb. Comp. 42 (2002), 113-125.
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  90. Continued fractions, fibered automata, and a theorem of Rosenberg, Multiple-Valued Logic 8 (2002), 503-515.
  91. A coalgebraic approach to quasigroup permutation representations, Algebra Universalis 48 (2002), 427-438.
    Available online.
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  92. (with M.A. Akivis et al.) Alexander M. Shelekhov, Webs and Quasigroups, 2002, 7-10.
  93. Greedy loop transversal codes (conference report), Proceedings of the Fortieth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 2003, 1458-9.
  94. (with D.-H. Choi) Greedy loop transversal codes for correcting error bursts, Discrete Math. 264 (2003), 37-43.
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  95. (with J.Y. Choi) On the unimodality and combinatorics of Bessel numbers, Discrete Math. 264 (2003), 45-53.
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  96. Time in biology and physics, pp. 145-152 in "The Nature of Time: Geometry, Physics and Perception" (eds. R. Buccheri, M. Saniga, W.M. Stuckey), Kluwer, Dordrecht, 2003.
    Available online.
  97. Permutation representations of loops, J. Algebra 264 (2003), 342-357. Available online.
  98. On the dimension of finite permutation group actions, Beiträge zur Algebra und Geometrie 44 (2003), 99-109.
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  99. Quasigroup permutation representations, Quasigroups and Related Systems 10 (2003), 115-134. Online abstract.
  100. (with K.J. Pszczoła and A.B. Romanowska) Duality for some free modes, Discuss. Math. Gen. Alg. and Appl. 23 (2003), 45-61. Available online.
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  101. (with D.-H. Choi) Support functions of general convex sets, Algebra Universalis 49 (2003), 305-319.
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  102. On the characterisation of Mal'tsev and Jónsson-Tarski Algebras, Discuss. Math. Gen. Alg. and Appl. 23 (2003), 149-161.
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  103. (with B. Im) Simple ternary Grassmann algebras, Alg. Colloq. 11 (2004), 223-230.
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  104. A macroscopic approach to demography, J. Math. Biol. 48 (2004), 105-118.
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  105. (with K.J. Pszczoła and A.B. Romanowska) Duality for quadrilaterals, Contributions to General Algebra 13 (2004), 127-134. Available online.
  106. (with B. Im) Orthogonal ternary algebras and Thomas sums, Alg. Colloq. 11 (2004), 287-296.
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  107. (with K.W. Johnson) Characters of finite quasigroups VII: permutation characters, Comment. Math. Univ. Carol. 45 (2004), 265-273. Available online.
  108. (with B. Kivunge) Subloops of sedenions, Comment. Math. Univ. Carol. 45 (2004), 295-302. Available online.
  109. Representation theory of quasigroups, Sci. Math. Japonicae 60 (2004), 171-204 (invited survey paper).
  110. The Burnside algebra of a quasigroup, J. Algebra 279 (2004), 383-401. Available online.
  111. Characters of central piques, J. Algebra 279 (2004), 437-450.
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  112. Extension theory in Mal'tsev varieties, pp. 517-522 in "Galois Theory, Hopf Algebras, and Semiabelian Categories" (eds. G. Janelidze, B. Pareigis and W. Tholen), Fields Institute Communications Volume 43, 2004.
  113. (with B. Im) Comtrans algebras, Thomas sums and bilinear forms, Arch. Math. 84 (2005), 107-117.
    Available online.
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  114. Patterns of information storage and senescence, in "Proceedings of FIS2005, The Third Conference on the Foundations of Information Science, Paris, July 4-7, 2005" (ed. M. Petitjean), Electronic Edition, ISBN 3-906980-17-0. Available online.
  115. (with J.Y. Choi) On the combinatorics of multi-restricted numbers, Ars Combin. 75 (2005), 45-63.
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  116. Symmetry and entropy: a hierarchical perspective, Symmetry: Culture and Science 16 (2005), 37-45.
  117. (with B. Im) Trilinear forms and the space of comtrans algebras, Honam Math. J. 27 (2005), 595-602.
  118. (with J.Y. Choi, L. Long and S.-H. Ng) Reciprocity for multirestricted Stirling numbers, J. Combin. Theory Ser. A 113 (2006), 1050-1060. Available online.
  119. Permutation representations of left quasigroups, Algebra Universalis 55 (2006), 387-406.
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  120. (with A.B. Romanowska) Duality for central piques, Quasigroups and Related Systems 14 (2006), 81-89.
  121. (with J.Y. Choi) Recurrences for tri-restricted numbers, J. Comb. Math. Comb. Comp. 58 (2006), 3-11.
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  122. Quasigroups and approximate symmetry, J. Comb. Math. Comb. Comp. 58 (2006), 55-64.
  123. (with Yu.M. Movsisyan and A.B. Romanowska) Superproducts, hyperidentities, and algebraic structures of logic programming, J. Comb. Math. Comb. Comp. 58 (2006), 101-111.
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  124. (with R. Aydinyan) Loop transversal codes for error detection, J. Comb. Math. Comb. Comp. 58 (2006), 153-159.
  125. (with G. Bińczak and A.B. Romanowska) Poset extensions, convex sets, and semilattice presentations, Discrete Math. 307 (2007), 1-11.
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  126. Four lectures on quasigroup representations, Quasigroups and Related Systems 15 (2007), 11-42.
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  127. Axiomatization of quasigroups, Discuss. Math. Gen. Alg. and Appl. 27 (2007), 21-33. Available online.
  128. (with E. Orłowska and A.B. Romanowska) Abstract barycentric algebras, Fund. Informaticae 81 (2007), 257-273.
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  129. (with K.W. Johnson) On the category of weak Cayley table morphisms between groups, Selecta Mathematica 13 (2007), 57-67.
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  130. (with B. Im and H. Ko) Semisymmetrizations of abelian group isotopes, Taiwanese J. Math. 11 (2007), 1529-1534.
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  131. Evans' Normal Form Theorem revisited, Internat. J. Algebra Comput. 17 (2007), 1577-1592.
    * Electronic version of an article published as
    Int. J. Alg. & Comp. 17 No. 8 (2007), 1577-1592.
    DOI 10.1142/S0218196707004323.
    © World Scientific Publishing Company
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  132. (with B. Im) Generic adjoints in comtrans algebras of bilinear spaces, Linear Algebra Appl. 428 (2008), 953-961. Available online.
  133. Ternary quasigroups and the modular group, Comment. Math. Univ. Carol. 49 (2008), 309-317.
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  134. (with M. Dağlı and D. D'Alessandro) A general framework for recursive decompositions of unitary quantum evolutions, J. Phys. A: Math. Theor. 41 (2008).
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  135. (with K.O. Chung) Weak homomorphisms and graph coalgebras, Arabian J. Sci. and Eng. 33 (2008), 107-122.
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  136. Quasigroup homotopies, semisymmetrization, and reversible automata, Internat. J. Algebra Comput. 18 (2008), 1203-1221.
    * Electronic version of an article published as
    Int. J. Alg. & Comp. 18 No. 7 (2008), 1203-1221.
    DOI 10.1142/S0218196708004846.
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  137. (with B. Im) Trilinear products and comtrans algebra representations, Linear Algebra Appl. 430 (2009), 17-26. Available online.
  138. (with D. Doan et al.) Partial semigroups and primality indicators in the fractal generation of binomial coefficients to a prime square modulus, Demonstr. Math. 42 (2009), 21-37.
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  139. (with A.B. Romanowska) Barycentric algebras and gene expression, pp. 20-27 in "WILF 2009" (eds. V. di Gesù, S.K. Pal and A. Petrosino), Springer Lecture Notes in Artificial Intelligence, Berlin, 2009.
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  140. (with A. Romanowska and P. Ślusarski) Duality for convex polytopes, J. Australian Math. Soc. 86 (2009), 399-412.
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  141. * NOTICE: this is the authors' version
    (with updated bibliography)
    of a work that was accepted for publication
    in Journal of Combinatorial Theory, Series A.
    Changes resulting from the publishing process,
    such as peer review, editing, corrections,
    structural formatting, and other quality
    control mechanisms may not be reflected
    in this document. Changes may have been
    made to this work since it was submitted for
    publication. A definitive version was
    subsequently published in J. Combin. Theory
    Ser. A 117 (2010), 790-798. DOI#
    doi:10.1016/j.jcta.2009.10.015
    (with K.W. Johnson) On the smallest simple, unipotent Bol loop, J. Combin. Theory Ser. A 117 (2010), 790-798.
    Available online.
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  142. (with B. Kerby) Quasigroup automorphisms and symmetric group characters, Comment. Math. Univ. Carol. 51 (2010), 279-286.
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  143. (with B. Kerby) Quasigroup automorphisms and the Norton-Stein complex, Proc. Amer. Math. Soc. 138 (2010), 3079-3088.
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  144. * Electronic version of an article published in
    Math. Proc. Camb. Phil. Soc. 149 No. 3 (2010), 445-453.
    DOI 10.1017/S0305004110000393.
    © Cambridge University Press
    http://dx.doi.org/doi:10.1017/S0305004110000393
    (with L. Long) Catalan loops, Math. Proc. Camb. Phil. Soc. 149 (2010), 445-453.
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  145. * Author Posting. © Informa plc, 2010.
    This is the authors' version of the work.
    It is posted here by permission of Informa plc
    for personal use, not for redistribution.
    The definitive version was published in
    Communications in Algebra,
    Volume 38 Issue 8, August 2010.
    doi:10.1080/00927870903095590
    (with K.W. Johnson) Matched pairs, permutation representations, and the Bol property, Comm. Algebra 38 (2010), 2903-2914.
    Available online.
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  146. On groups of hypersubstitutions, Algebra Universalis 64 (2010), 39-48.
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  147. (with B. Im and J.-Y. Ryu) Sharply transitive sets in quasigroup actions, J. Alg. Comb. 33 (2011), 81-93.
    Available online.
  148. * NOTICE: this is the authors' version
    of a work that was accepted for publication
    in Journal of Combinatorial Theory, Series A.
    Changes resulting from the publishing process,
    such as peer review, editing, corrections,
    structural formatting, and other quality
    control mechanisms may not be reflected
    in this document. Changes may have been
    made to this work since it was submitted for
    publication. A definitive version was
    subsequently published in J. Combin. Theory
    Ser. A 118 (2011), 2232-2245. DOI#
    doi:10.1016/j.jcta.2011.05.003
    (with B. Kerby) A graph-theoretic approach to quasigroup cycle numbers, J. Combin. Theory Ser. A 118 (2011), 2232-2245.
    Available online.
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    (with correction to Example 7.2.)



  149. * Electronic version of an article published as
    Int. J. Alg. & Comp. 21 No. 3 (2011), 387-408.
    DOI 10.1142/S0218196711006248.
    © World Scientific Publishing Company
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    (with K. Matczak and A.B. Romanowska) Dyadic polygons, Internat. J. Algebra Comput. 21 (2011), 387-408.
    Available online.
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  150. * Electronic version of an article published as
    Int. J. Alg. & Comp. 21 No. 3 (2011), 459-472.
    DOI 10.1142/S0218196711006315.
    © World Scientific Publishing Company
    http://www.worldscinet.com/ijac/ijac.shtml
    (with B. Im) Representation theory for varieties of comtrans algebras and Lie triple systems, Int. J. Alg. & Comp. 21 (2011), 459-472.
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  151. Modes, modals, and barycentric algebras: a brief survey and an additivity theorem, Demonstr. Math. 44 (2011), 571-587.
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  152. * Electronic version of an article published as
    Algebra Universalis 66 (2011), 35-48.
    DOI 10.1007/s00012-011-0140-5.
    The final publication is available
    at www.springerlink.com.
    Lambda-rings of automorphisms, Algebra Universalis 66 (2011), 35-48.
    Available online.
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  153. * NOTICE: this is the author's version
    of a work that was accepted for publication
    in the Journal of Pure and Applied Algebra.
    Changes resulting from the publishing process,
    such as peer review, editing, corrections,
    structural formatting, and other quality
    control mechanisms may not be reflected
    in this document. Changes may have been
    made to this work since it was submitted for
    publication. A definitive version was
    subsequently published in J. Pure Appl. Alg.
    216 (2012), 811-825. DOI#
    doi.org/10.1016/j.jpaa.2011.08.014
    Groups, triality, and hyperquasigroups, J. Pure Appl. Alg. 216 (2012), 811-825.
    Available online.
    Click here for local copy.*




  154. Homotopies of central quasigroups, Comm. Algebra 40 (2012), 1878-1885.
    Available online.
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  155. On 2-Engel groups and Bruck loops, J. Group Theory 16 (2013), 87-106.
    Available online.
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  156. (with A. Mućka and A.B. Romanowska) Many-sorted and single-sorted algebras, Algebra Universalis 69 (2013), 171-190.
    Available online.
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  157. On the algebraic structure of Dyson's Circular Ensembles, Sci. Math. Japonicae 76 (2013), 289-298.
    Available online.
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  158. (with A.B. Romanowska) Entropic Hopf algebras, pp. 187-190 in "TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic" (N. Galatos, A. Kurz, C. Tsinakis, eds.), Easychair Proceedings in Computing 25, 2014.
    Available online.
  159. (with K.V. Adaricheva and A.B. Romanowska) The algebra of mode homomorphisms, Open Mathematics/Cent. Eur. J. Math. 12 (2014), 1265-1277. Available online.
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  160. Ricci curvature, circulants, and a matching condition, Discrete Math. 329 (2014), 88-98.
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  161. Palindromic and sudoku quasigroups, J. Comb. Math. Comb. Comp. 88 (2014), 85-94.
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  162. (with K. Matczak) Undirected replicas of directional binary algebras, J. of Algebra and its Applications 13, 1450051 (2014) [19 pages].
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  163. (with K.W. Johnson and M. Munywoki) The upper triangular algebra loop of degree 4, Comment. Math. Univ. Carol. 55 (2014), 457-470.
    Available online.
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  164. (with C. Zhang) Parametrizing the net maternity function, Letters in Biomathematics 1 (2014), 181-192.
    Available online.
  165. (with P.K. Jha) Cycle Kronecker products that are representable as optimal circulants, Discrete Appl. Math. 181 (2015), 130-138.
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  166. Sylow theory for quasigroups, J. Combin. Designs 23 (2015), 115-133.
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  167. (with C. Zhang) Generalized Lotka stability, Theor. Pop. Biol. 103 (2015), 38-43.
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  168. (with A.B. Romanowska) On Hopf algebras in entropic Jónsson-Tarski varieties, Bull. Korean Math. Soc. 52 (2015), 1587-1606.
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  169. One-sided quantum quasigroups and loops, Demonstr. Math. 48 (2015), 620-636.
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  170. Directional algebras, Houston J. Math. 42 (2016), 1-22.
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  171. Quantum quasigroups and loops, J. Algebra 456 (2016), 46-75.
    Available online.
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  172. (with M. Dağlı and L.A. Garcia) Restricted comtrans algebras over small odd primes, Comm. Algebra 44 (2016), 4220-4242.
    Available online.
  173. Quantum idempotence, distributivity, and the Yang-Baxter equation, Comment. Math. Univ. Carol. 57 (2016), 567-583.
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  174. Conformal algebras, vertex algebras, and the logic of locality, Math. Slovaca 66 (2016), 407-420.
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  175. Belousov's Theorem and the quantum Yang-Baxter equation, Bulletinul Academiei de Ştiinţe a Republicii Moldovei. Matematica 80 (2016), 7-23.
    Available online.
  176. Quantum quasigroups and the quantum Yang-Baxter equation, Axioms 5(4) (2016), 25.
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  177. (with M.K. Kinyon and P. Vojtĕchovský) Sylow theory for quasigroups II: Sectional action, J. Combin. Designs 25 (2017), 159-184.
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  178. (with H.-Y. Lee and B. Im) Stochastic tensors and approximate symmetry, Discrete Math. 340 (2017), 1335-1350.
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  179. (with B. Im and K. Matczak) Linear diquasigroups, J. of Algebra and its Applications, 16, 1750057 (2017) [20 pages].
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  180. Burnside orders, Burnside algebras and partition lattices, Order, 34 (2017), 253-263. doi:10.1007/s11083-016-9397-9.
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  181. Poset loops, Order, 34 (2017), 265-285. doi:10.1007/s11083-016-9398-8.
    Click here for an open view of the published copy.
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  182. (with A.B. Romanowska) Duality for quasilattices and Galois connections, Fund. Informaticae 156 (2017), 331-359.
    Available online.
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  183. (with A.B. Romanowska) Diagrammatic duality, pp. 273-295 in "Don Pigozzi on Abstract Algebraic Logic" (J. Czelakowski, ed.), Outstanding Contributions to Logic 16, Springer, Berlin, 2018.
    ISBN 978-3-319-74771-2.
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  184. (with A. Komorowski and A.B. Romanowska) Keimel's problem on the algebraic axiomatization of convexity, Algebra Universalis (2018) 79:22.
    Available online.
    Click here for errata.
  185. *The Version of Record of this manuscript
    has been published and is available in
    Communications in Algebra ,
    Volume 46 Issue 11, September 2018.
    (with U.N. Iyer and E.J. Taft) One-sided Hopf algebras and quantum quasigroups, Comm. Algebra 46 (2018), 4590-4608.
    Available online.
    Click here for local copy.*
  186. (with B. Im) Orthogonality of approximate Latin squares and quasigroups, pp. 165-181 in "Nonassociative Mathematics and its Applications" (P. Vojtĕchovský et al., eds.), Contemporary Mathematics 721, American Mathematical Society, Providence, RI, 2019. ISBN 978-1-4704-4245-3.
  187. (with M. Dağlı and O. Olmez) Ricci curvature, circulants, and extended matching conditions, Bull. Korean Math. Soc. 56 (2019), 201-217.
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  188. (with G.N. Nop) Higher homotopy, J. Algebra 526 (2019), 309-332.
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  189. (with A. Komorowski and A.B. Romanowska) Barycentric algebras and beyond, Algebra Universalis (2019), 80:20.
    Available online.
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  190. (with G.N. Nop and A.B. Romanowska) Category theory as a foundation for the concept analysis of complex systems and time series, pp. 119-134 in "Category Theory in Physics, Mathematics, and Philosophy" (M. Kuś and B. Skowron, eds.), Springer Proceedings in Physics 235, 2019.
  191. (with S.G. Wang) Isomorphism invariants for linear quasigroups, São Paulo J. Math. Sci. 14 (2020), 152–164.
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  192. Augmented quasigroups and character algebras, Adv. Math. 363 (2020), 106983.
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  193. Quasigroups, hyperquasigroups, and vector spaces over fields with one or more elements, pp. 382-407 in "New Trends in Algebras and Combinatorics" (K.-P. Shum et al., eds.), World Scientific, Singapore, 2020.
    Available online.
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  194. (with M. Dağlı and B. Im) Linear and non-linear loop transversal codes in error-correction and graph domination, Bull. Korean Math. Soc. 57 (2020), 295-309.
    Available online.
  195. (with S.G. Wang) On the enumeration and asymptotic growth of free quasigroup words, Internat. J. Algebra Comput. 30 (2020), 1645-1683.
    https://doi.org/10.1142/S0218196720500496.
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  196. Semisymmetrization and Mendelsohn quasigroups, Comment. Math. Univ. Carol. 61 (2020), 553–566.
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  197. (with B. Im and A. Nowak) Algebraic properties of quantum quasigroups, J. Pure Appl. Algebra 225 (2021), 106539.
    https://doi.org/10.1016/j.jpaa.2020.106539.
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  198. *This article may be downloaded
    for personal use only.
    Any other use requires prior permission
    of the author and AIP Publishing.
    This article appeared in
    AVS Quantum Science,
    Volume 3 (2021), 044101
    and may be found at
    doi.org/10.1116/5.0065951
    (with G.N. Nop and D. Paudyal) Ytterbium ion trap quantum computing: the current state of the art,
    AVS Quantum Sci. 3 (2021), 044101. https://doi.org/10.1116/5.0065951.
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  199. (with B. Song, L. Luo and J. Wang) Geometric pumping and dephasing at topological transition, Phys. Rev. B 105, 035101 (2022).
    https://doi.org/10.1103/PhysRevB.105.035101.
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  200. (with B. Im) Homogeneous conditions for stochastic tensors, Comm. Korean Math. Soc. 37 (2022), 371-384.
    https://doi.org/10.4134/CKMS.c210127
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  201. (with P. Vojtĕchovský) Okubo quasigroups, Doc. Math. 27 (2022), 535-580.
    https://doi.org/10.25537/dm.2022v27.535-580
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  202. Cayley theorems for Loday algebras, Results Math. 77, Article 218, (2022).
    https://doi.org/10.1007/s00025-022-01748-8
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  203. (with S.G. Wang) Quasigroup words and reversible automata, J. Mult.-Valued Logic Soft Comput. 39 (2022), 135-157.
    Click here for preprint version.
  204. (with B. Im) Cross-intercalates and geometry of short extreme points in the Latin polytope of degree 3, J. Korean Math. Soc. 60 (2023), 91-113.
    https://doi.org/10.4134/JKMS.j220182
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  205. (with Z. Yang) Phase transition and time emergence in a statistical model of species competition, Results in Physics 44 (2023), 106178.
    https://doi.org/10.1016/j.rinp.2022.106178
    Available online.
  206. (with J.A. Stevenson) Character groups of dihedral and generalized quaternion groups, J. Algebra Appl. 22 (2023), 2350141 (24 pages).
    https://www.worldscientific.com/doi/10.1142/S0219498823501414
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  207. (with B. Im) Combinatorial supersymmetry: Supergroups, superquasigroups, and their multiplication groups, J. Korean Math. Soc. 61 (2024), 109-132.
    Available online.
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  208. (with C.M. Depies and M.D. Ashburn) Octonions as Clifford-like algebras, J. Algebra 644 (2024), 761-795.
    Available online.
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  209. (with G.N. Nop) Quasilattices and complex concept analysis, Quaest. Math. 47 (2024), 173-200.
    https://doi.org/10.2989/16073606.2023.2205034
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  210. (with G.N. Nop, D. Paudyal and D. Stick) Bilayer Ion Trap Design for 2D Arrays, Quantum Sci. Technol., to appear.
    https://doi.org/10.1088/2058-9565/ad3f43
    Available online.
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  211. (with B. Song, L. Luo and J. Wang) Quantum Liouville theorem based on Haar measure, Phys. Rev. B, to appear.
    Click here for local copy.
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