Abstract :
[en] 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.
Scopus citations®
without self-citations
2