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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16387 |
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| _version_ | 1866914846921981952 |
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| author | Abram, Antoine Hivert, Florent Mitchell, James D. Novelli, Jean-Christophe Tsalakou, Maria |
| author_facet | Abram, Antoine Hivert, Florent Mitchell, James D. Novelli, Jean-Christophe Tsalakou, Maria |
| contents | In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations $a^{σ(a)} = a$ with $σ(a)\ge 2$ for every generator $a$. The starting point for this description is the recent paper of Abram and Reutenauer about the so-called stylic monoid which happens to be the quotient of the plactic monoid by the relations $a^2 = a$ for every letter $a$. The plactic-like monoids considered are the plactic monoid itself, the Chinese monoid, and the sylvester monoid. In each case we describe: a set of normal forms, and the idempotents; and obtain formulae for their size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power Quotients of Plactic-like Monoids Abram, Antoine Hivert, Florent Mitchell, James D. Novelli, Jean-Christophe Tsalakou, Maria Combinatorics In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations $a^{σ(a)} = a$ with $σ(a)\ge 2$ for every generator $a$. The starting point for this description is the recent paper of Abram and Reutenauer about the so-called stylic monoid which happens to be the quotient of the plactic monoid by the relations $a^2 = a$ for every letter $a$. The plactic-like monoids considered are the plactic monoid itself, the Chinese monoid, and the sylvester monoid. In each case we describe: a set of normal forms, and the idempotents; and obtain formulae for their size. |
| title | Power Quotients of Plactic-like Monoids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.16387 |