Article (Scientific journals)
Every quasitrivial n-ary semigroup is reducible to a semigroup
Couceiro, Miguel; DEVILLET, Jimmy
2019In Algebra Universalis, 80 (4)
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Keywords :
quasitrivial polyadic semigroup; reducibility; unique reduction; symmetry; enumeration
Abstract :
[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 :
Mathematics
Author, co-author :
Couceiro, Miguel
DEVILLET, Jimmy ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Every quasitrivial n-ary semigroup is reducible to a semigroup
Publication date :
December 2019
Journal title :
Algebra Universalis
ISSN :
1420-8911
Publisher :
Birkhauser Verlag, Switzerland
Volume :
80
Issue :
4
Peer reviewed :
Peer Reviewed verified by ORBi
FnR Project :
FNR10949314 - Geometric And Stochastic Methods In Mathematics And Applications, 2015 (01/10/2016-31/03/2023) - Gabor Wiese
Funders :
FNR - Fonds National de la Recherche [LU]
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since 12 April 2019

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