All quasitrivial n-ary semigroups are reducible to semigroups - Inria - Institut national de recherche en sciences et technologies du numérique
Pré-Publication, Document De Travail Année : 2019

All quasitrivial n-ary semigroups are reducible to semigroups

Résumé

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.
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Dates et versions

hal-02099236 , version 1 (14-04-2019)
hal-02099236 , version 2 (29-08-2019)

Identifiants

  • HAL Id : hal-02099236 , version 1

Citer

Miguel Couceiro, Jimmy Devillet. All quasitrivial n-ary semigroups are reducible to semigroups. 2019. ⟨hal-02099236v1⟩
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