Work

Power Quotients of Plactic-like Monoids

Year: 2024

Type: article

Abstract: In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations $a^{\sigma(a)} = a$ with $\sigma(a)\ge 2$ 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.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.403.7

Authors: Antoine Abram, Florent Hivert, James D. Mitchell, Jean-Christophe Novelli, Maria Tsalakou

Institutions: Université du Québec à Montréal, University of St Andrews, Université Paris-Saclay, Laboratoire Interdisciplinaire des Sciences du Numérique, Laboratoire d'Informatique Gaspard-Monge, Université Gustave Eiffel

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Natural Sciences and Engineering Research Council of Canada

OpenAlex ID: W4399803900

FWCI:

Cites: 10

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Related to: 10