# Algorithm for the complement of orthogonal operations

Commentationes Mathematicae Universitatis Carolinae (2018)

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

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topFryz, 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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