All quasitrivial n-ary semigroups are reducible to semigroups

Miguel Couceiro (1) , Jimmy Devillet (2)

1 ORPAILLEUR - Knowledge representation, reasonning
2 FSTC - Faculty of Science, Technology and Communication [Luxembourg]

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]

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