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Quasitrivial semigroups: Characterizations and enumerations

Miguel Couceiro 1 Jimmy Devillet 2 Jean-Luc Marichal 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
2 FSTC - Faculty of Science, Technology and Communication [Luxembourg]
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.
Keywords : Quasitrivial semigroup Quasitrivial and order-preserving semigroup Enumeration of quasitrivial semigroups Single-peaked ordering Single-plateaued weak ordering Quasitrivial and commutative semigroup
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https://hal.inria.fr/hal-01826868
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Submitted on : Monday, July 2, 2018 - 3:53:23 PM
Last modification on : Friday, November 8, 2019 - 3:06:02 PM
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Miguel Couceiro, Jimmy Devillet, Jean-Luc Marichal. Quasitrivial semigroups: Characterizations and enumerations. Semigroup Forum, Springer Verlag, 2019, 98 (3), pp.472-498. ⟨10.1007/s00233-018-9928-3⟩. ⟨hal-01826868v2⟩

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