Groups of permutations that are even on maximal proper subsets, and related monoids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909037838204928 |
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| author | Fernandes, Vítor H. |
| author_facet | Fernandes, Vítor H. |
| contents | Let $n$ be a positive integer and let $[n]=\{1,2,\ldots,n\}$. Let $Γ_n$ denote the group of permutations on $[n]$ whose restrictions to maximal proper subsets of $[n]$ are even, let $Σ_n$ denote the monoid of transformations on $[n]$ whose injective restrictions to maximal proper subsets of $[n]$ are even and let $Δ_n$ denote the submonoid of $Σ_n$ generated by transformations of rank at least $n-1$. In this paper, we present descriptions of $Γ_n$, $Δ_n$ and $Σ_n$, determine their cardinalities and ranks, and provide minimal generating sets for each of them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12342 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Groups of permutations that are even on maximal proper subsets, and related monoids Fernandes, Vítor H. Rings and Algebras 20M20, 20M10, 20B35 Let $n$ be a positive integer and let $[n]=\{1,2,\ldots,n\}$. Let $Γ_n$ denote the group of permutations on $[n]$ whose restrictions to maximal proper subsets of $[n]$ are even, let $Σ_n$ denote the monoid of transformations on $[n]$ whose injective restrictions to maximal proper subsets of $[n]$ are even and let $Δ_n$ denote the submonoid of $Σ_n$ generated by transformations of rank at least $n-1$. In this paper, we present descriptions of $Γ_n$, $Δ_n$ and $Σ_n$, determine their cardinalities and ranks, and provide minimal generating sets for each of them. |
| title | Groups of permutations that are even on maximal proper subsets, and related monoids |
| topic | Rings and Algebras 20M20, 20M10, 20B35 |
| url | https://arxiv.org/abs/2605.12342 |