6 papers · 1 filter
On the structure of symmetric -ary bands
Jimmy Devillet, Pierre Mathonet
We study the class of symmetric -ary bands. These are -ary semigroups such that is invariant under the action of permutations and idempotent, i.e., satisfies $F(x…
Every quasitrivial n-ary semigroup is reducible to a semigroup
Miguel Couceiro, Jimmy Devillet
We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These resu…
Classifications of quasitrivial semigroups
Jimmy Devillet, Jean-Luc Marichal, Bruno Teheux
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is…
Characterizations of biselective operations
Jimmy Devillet, Gergely Kiss
Let be a nonempty set and let . We say that a binary operation is -selective if for all $x…
Associative, idempotent, symmetric, and order-preserving operations on chains
Jimmy Devillet, Bruno Teheux
We characterize the associative, idempotent, symmetric, and order-preserving operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilat…
Bisymmetric and quasitrivial operations: characterizations and enumerations
Jimmy Devillet
We investigate the class of bisymmetric and quasitrivial binary operations on a given set and provide various characterizations of this class as well as the subclass of bisymme…