Quasitrivial semigroups: characterizations and enumerations

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.

References in corpus (2)

• Characterizations of idempotent discrete uninorms
• Single-Peaked Consistency for Weak Orders Is Easy

Cited by in corpus (2)

• Classifications of quasitrivial semigroups
• Reducibility of $n$-ary semigroups: from quasitriviality towards idempotency