Every quasitrivial n-ary semigroup is reducible to a semigroup
Rings and Algebras
2019-09-24 v2 Discrete Mathematics
Combinatorics
Abstract
We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary semigroups. We also explicitly determine the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer sequences.
Keywords
Cite
@article{arxiv.1904.05968,
title = {Every quasitrivial n-ary semigroup is reducible to a semigroup},
author = {Miguel Couceiro and Jimmy Devillet},
journal= {arXiv preprint arXiv:1904.05968},
year = {2019}
}