Algorithm for the complement of orthogonal operations

Iryna V. Fryz

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 2, page 135-151
  • ISSN: 0010-2628

Abstract

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G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a k -tuple of orthogonal n -ary operations, where k < n , to an n -tuple of orthogonal n -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k -tuple of orthogonal n -ary operations to an n -tuple of orthogonal n -ary operations and an algorithm for complementing a k -tuple of orthogonal k -ary operations to an n -tuple of orthogonal n -ary operations. Also we find some estimations of the number of complements.

How to cite

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Fryz, Iryna V.. "Algorithm for the complement of orthogonal operations." Commentationes Mathematicae Universitatis Carolinae 59.2 (2018): 135-151. <http://eudml.org/doc/294417>.

@article{Fryz2018,
abstract = {G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a $k$-tuple of orthogonal $n$-ary operations, where $k<n$, to an $n$-tuple of orthogonal $n$-ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a $k$-tuple of orthogonal $n$-ary operations to an $n$-tuple of orthogonal $n$-ary operations and an algorithm for complementing a $k$-tuple of orthogonal $k$-ary operations to an $n$-tuple of orthogonal $n$-ary operations. Also we find some estimations of the number of complements.},
author = {Fryz, Iryna V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {orthogonality of operations; retract orthogonality of operations; complement of orthogonal operations; block-wise recursive algorithm},
language = {eng},
number = {2},
pages = {135-151},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Algorithm for the complement of orthogonal operations},
url = {http://eudml.org/doc/294417},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Fryz, Iryna V.
TI - Algorithm for the complement of orthogonal operations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 2
SP - 135
EP - 151
AB - G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a $k$-tuple of orthogonal $n$-ary operations, where $k<n$, to an $n$-tuple of orthogonal $n$-ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a $k$-tuple of orthogonal $n$-ary operations to an $n$-tuple of orthogonal $n$-ary operations and an algorithm for complementing a $k$-tuple of orthogonal $k$-ary operations to an $n$-tuple of orthogonal $n$-ary operations. Also we find some estimations of the number of complements.
LA - eng
KW - orthogonality of operations; retract orthogonality of operations; complement of orthogonal operations; block-wise recursive algorithm
UR - http://eudml.org/doc/294417
ER -

References

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  1. Aczél J., Dhombres J., Functional Equations in Several Variables, With applications to Mathematics, Information Theory and to the Natural and Social Sciences. Encyclopedia of Mathematics and Its Applications, 31, Cambridge University Press, Cambridge, 1989. MR1004465
  2. Bektenov A. S., Jakubov T., Systems of orthogonal n -ary operations, Bul. Akad. Štiince RSS Moldoven. (1974), no. 3, 7–14, 93 (Russian). MR0360905
  3. Belyavskaya G. B., Mullen G. L., Orthogonal hypercubes and n -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86. Zbl1101.20049MR2206148
  4. Couselo E., Gonzalez S., Markov V., Nechaev A., 10.1515/dma.1998.8.3.217, Discrete Math. Appl. 8 (1998), no. 3, 217–245; doi: 10.1515/dma.1998.8.3.217. MR1673150DOI10.1515/dma.1998.8.3.217
  5. Dougherty S. T., Szczepanski T. A., Latin k -hypercubes, Australas. J. Combin. 40 (2008), 145–160. MR2381422
  6. Ethier J. T., Mullen G. L., 10.1016/j.disc.2012.03.008, Discrete Math. 312 (2012), no. 12–13, 2050–2061; doi: 10.1016/j.disc.2012.03.008. MR2920865DOI10.1016/j.disc.2012.03.008
  7. Evans T., 10.1007/BF01835999, Aequationes Math. 14 (1976), no. 3, 485–491. MR0414396DOI10.1007/BF01835999
  8. Fryz I. V., Orthogonality and retract orthogonality of operations, to appear in Bul. Akad. Štiince RSS Moldoven. 
  9. Fryz I. V., Sokhatsky F. M., 10.1016/j.disc.2016.11.012, Discrete Math. 340 (2017), no. 8, 1957–1966; doi: 10.1016/j.disc.2016.11.012. MR3648223DOI10.1016/j.disc.2016.11.012
  10. Keedwell A. D., Dénes J., Latin Squares and Their Applications, Elsevier/North Holland, Amsterdam, 2015. MR3495977
  11. Markovski S., Mileva A., 10.2298/PIM1715109M, Publ. Inst. Math. (Beograd) (N.S.) 101(115) (2017), 109–119; doi: 10.2298/PIM1715109M. MR3700406DOI10.2298/PIM1715109M
  12. Sokhatsky F. M., Krainichuk H. V., Solution of distributive-like quasigroup functional equations, Comment. Math. Univ. Carolin. 53 (2012), no. 3, 447–459. MR3017842
  13. Trenkler M., 10.1007/s10587-005-0060-7, Czechoslovak Math. J. 55(130) (2005), no. 3, 725–728; doi: 10.1007/s10587-005-0060-7. MR2153097DOI10.1007/s10587-005-0060-7

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