PreprintCC BY-NC-ND 4.0arXiv
Power quotients of plactic-like monoids
Abstract
In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations aσ(a) = a for σ(a) ≥ 2 for every generator a. The starting point of this paper is the recent paper of Reutenauer and the first author about the stylic monoid. This monoid is the quotient of the plactic monoid by the relations a2 = a for every generator a. The plactic-like monoids considered here are the plactic monoid itself, the Chinese monoid, the hypoplactic monoid, the sylvester monoid, the metasylvester and hyposylvester monoids. In each case we describe a set of normal forms and the idempotents. We obtain formulae for their cardinalities and we describe their isomorphism types.
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BibTeX
@misc{abram2026power,
title = {{Power quotients of plactic-like monoids}},
author = {Antoine Abram and Florent Hivert and James D. Mitchell and Jean-Christophe Novelli and Maria Tsalakou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20317},
eprint = {2610.20317},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20317},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Power quotients of plactic-like monoids
AU - Antoine Abram
AU - Florent Hivert
AU - James D. Mitchell
AU - Jean-Christophe Novelli
AU - Maria Tsalakou
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20317
UR - https://arxiv.org/abs/2610.20317
AB - In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations a^σ(a) = a for σ(a) ≥ 2 for every generator a. The starting point of this paper is the recent paper of Reutenauer and the first author about the stylic monoid. This monoid is the quotient of the plactic monoid by the relations a^2 = a for every generator a. The plactic-like monoids considered here are the plactic monoid itself, the Chinese monoid, the hypoplactic monoid, the sylvester monoid, the metasylvester and hyposylvester monoids. In each case we describe a set of normal forms and the idempotents. We obtain formulae for their cardinalities and we describe their isomorphism types.
ER -