# Algorithm for the complement of orthogonal operations

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

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## 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, 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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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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