| Reference : Every quasitrivial n-ary semigroup is reducible to a semigroup |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/39337 | |||
| Every quasitrivial n-ary semigroup is reducible to a semigroup | |
| English | |
| Couceiro, Miguel [] | |
Devillet, Jimmy  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| Dec-2019 | |
| Algebra Universalis | |
| Birkhauser Verlag | |
| 80 | |
| 4 | |
| Yes (verified by ORBilu) | |
| International | |
| 0002-5240 | |
| 1420-8911 | |
| Switzerland | |
| [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 | |
| Researchers ; Professionals ; Students | |
| http://hdl.handle.net/10993/39337 | |
| 10.1007/s00012-019-0626-0 | |
| FnR ; FNR10949314 > Gabor Wiese > GSM > Geometric and Stochastic Methods in Mathematics and Applications > 01/10/2016 > 31/03/2023 > 2016 |
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