Quasitrivial semigroups: characterizations and enumerations
Miguel Couceiro, Jimmy Devillet, Jean‐Luc Marichal · HAL (Le Centre pour la Communication Scientifique Directe) · 2017
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.