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.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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