Every quasitrivial n-ary semigroup is reducible to a semigroup

Miguel Couceiro 1 Jimmy Devillet 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
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.
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Submitted on : Thursday, August 29, 2019 - 11:55:21 AM
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Miguel Couceiro, Jimmy Devillet. Every quasitrivial n-ary semigroup is reducible to a semigroup. Algebra Universalis, Springer Verlag, In press. ⟨hal-02099236v2⟩

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