[en] 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 results are then refined in the case of
symmetric n-ary semigroups. We also explicitly determine 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.
Disciplines :
Mathématiques
Auteur, co-auteur :
Couceiro, Miguel
DEVILLET, Jimmy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Every quasitrivial n-ary semigroup is reducible to a semigroup
Date de publication/diffusion :
décembre 2019
Titre du périodique :
Algebra Universalis
ISSN :
0002-5240
eISSN :
1420-8911
Maison d'édition :
Birkhauser Verlag, Suisse
Volume/Tome :
80
Fascicule/Saison :
4
Peer reviewed :
Peer reviewed vérifié par ORBi
Projet FnR :
FNR10949314 - Geometric And Stochastic Methods In Mathematics And Applications, 2015 (01/10/2016-31/03/2023) - Gabor Wiese
