Reference : All quasitrivial n-ary semigroups are reducible to semigroups
E-prints/Working papers : First made available on ORBilu
Physical, chemical, mathematical & earth Sciences : Mathematics
All quasitrivial n-ary semigroups are reducible to semigroups
Couceiro, Miguel []
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[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

File(s) associated to this reference

Fulltext file(s):

Open access
QuasitrivialNSem.pdfAuthor preprint418.56 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.