Publicação
On the cyclic inverse monoid on a finite set
| Resumo: | In this paper, we study the cyclic inverse monoid CIn on a set Ωn with n elements, i.e. the inverse submonoid of the symmetric inverse monoid on Ωn consisting of all restrictions of the elements of a cyclic subgroup of order n acting cyclically on Ωn. We show that CIn has rank 2 (for n ≥ 2) and n2n - n + 1 elements. Moreover, we give presentations of CIn on n+1 generators and 12 (n2 + 3n + 4) relations and on 2 generators and 12 (n2 - n + 6) relations. We also consider the remarkable inverse submonoid OCIn of CIn constituted by all its order-preserving transformations. We show that OCIn has rank n and 3 · 2n - 2n - 1 elements. Furthermore, we exhibit presentations of OCIn on n + 2 generators and 12 (n2 + 3n + 8) relations and on n generators and 12 (n2 + 3n) relations. |
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| Autores principais: | Fernandes, Vítor H. |
| Assunto: | cyclic group order-preserving orientation-preserving Partial permutations presentations rank General Mathematics |
| Ano: | 2024 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | In this paper, we study the cyclic inverse monoid CIn on a set Ωn with n elements, i.e. the inverse submonoid of the symmetric inverse monoid on Ωn consisting of all restrictions of the elements of a cyclic subgroup of order n acting cyclically on Ωn. We show that CIn has rank 2 (for n ≥ 2) and n2n - n + 1 elements. Moreover, we give presentations of CIn on n+1 generators and 12 (n2 + 3n + 4) relations and on 2 generators and 12 (n2 - n + 6) relations. We also consider the remarkable inverse submonoid OCIn of CIn constituted by all its order-preserving transformations. We show that OCIn has rank n and 3 · 2n - 2n - 1 elements. Furthermore, we exhibit presentations of OCIn on n + 2 generators and 12 (n2 + 3n + 8) relations and on n generators and 12 (n2 + 3n) relations. |
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