Representations and identities of involution Plactic-like monoids arising from the meet of the stalactic congruence and its dual
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911525276483584 |
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| author | Han, Bin Bin Zhang, Wen Ting Luo, Yan Feng |
| author_facet | Han, Bin Bin Zhang, Wen Ting Luo, Yan Feng |
| contents | Let $\mathsf{mSt}_n$ be the plactic-like monoid obtained by factoring the free monoid over a finite alphabet $\mathcal{A}_n$ by the meet of the stalactic congruence and its dual. In this paper, we prove that $\mathsf{mSt}_n$ can be equipped with multiple involutions, and divide these involutions into $\lfloor\frac{n}{2}\rfloor+1$ types. A faithful representation of $\mathsf{mSt}_n$ under each of these involutions is obtained. We give transparent combinatorial characterizations of identities for $\mathsf{mSt}_n$ under each involution, and so the finite basis problem and identity checking problem for them are solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representations and identities of involution Plactic-like monoids arising from the meet of the stalactic congruence and its dual Han, Bin Bin Zhang, Wen Ting Luo, Yan Feng Group Theory Let $\mathsf{mSt}_n$ be the plactic-like monoid obtained by factoring the free monoid over a finite alphabet $\mathcal{A}_n$ by the meet of the stalactic congruence and its dual. In this paper, we prove that $\mathsf{mSt}_n$ can be equipped with multiple involutions, and divide these involutions into $\lfloor\frac{n}{2}\rfloor+1$ types. A faithful representation of $\mathsf{mSt}_n$ under each of these involutions is obtained. We give transparent combinatorial characterizations of identities for $\mathsf{mSt}_n$ under each involution, and so the finite basis problem and identity checking problem for them are solved. |
| title | Representations and identities of involution Plactic-like monoids arising from the meet of the stalactic congruence and its dual |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.17473 |