Every quasitrivial n-ary semigroup is reducible to a semigroup

2019/04/11 by Miguel Couceiro, Couceiro, Miguel, Jimmy Devillet +1
Computer Science · Mathematics · #05A15 #16B99 #20M14 (Secondary) #20N15 (Primary) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Rings and Algebras (math.RA) #cs.DM #math.CO #math.RA #msc:05A15 #msc:16B99 #msc:20M14 #msc:20N15

paper · pdf · doi:10.48550/arxiv.1904.05968

arxiv created 2019/09/23 · arxiv updated 2019/09/24

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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