[en] Quasitrivial semigroup ; quasitrivial and commutative semigroup ; quasitrivial and order-preserving semigroups ; enumeration of quasitrivial semigroups ; single-peaked ordering ; single-plateaued weak ordering
[en] 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.
[LORIA, CNRS - Inria Nancy Grand Est - Université de Lorraine]
