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Journal Articles Semigroup Forum Year : 2019

Quasitrivial semigroups: Characterizations and enumerations

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Abstract

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly 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 and versions

hal-01826868 , version 1 (30-06-2018)
hal-01826868 , version 2 (02-07-2018)

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Miguel Couceiro, Jimmy Devillet, Jean-Luc Marichal. Quasitrivial semigroups: Characterizations and enumerations. Semigroup Forum, 2019, 98 (3), pp.472-498. ⟨10.1007/s00233-018-9928-3⟩. ⟨hal-01826868v2⟩
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