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Main Authors: Abram, Antoine, Hivert, Florent, Mitchell, James D., Novelli, Jean-Christophe, Tsalakou, Maria
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2406.16387
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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