Reference : Every quasitrivial n-ary semigroup is reducible to a semigroup
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Every quasitrivial n-ary semigroup is reducible to a semigroup
Couceiro, Miguel []
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
In press
Algebra Universalis
Birkhauser Verlag
[en] quasitrivial polyadic semigroup ; reducibility ; unique reduction ; symmetry ; enumeration
[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.
Fonds National de la Recherche - FnR

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