Power quotients of plactic-like monoids

Antoine Abram; Florent Hivert; James D. Mitchell; Jean-Christophe Novelli; Maria Tsalakou

doi:10.4204/eptcs.403.7

Power quotients of plactic-like monoids

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations aσ(a) = a with σ(a) ≥ 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 a2 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.

Original language	English
Title of host publication	Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings
Subtitle of host publication	Bordeaux, France, 24-28th June 2024
Editors	Srečko Brlek, Luca Ferrari
Publisher	Open Publishing Association
Pages	12–17
DOIs	https://doi.org/10.4204/eptcs.403.7
Publication status	Published - 24 Jun 2024
Event	Random Generation of Combinatorial Structures. Polyominoes and Tilings (GASCom 2024) - Bordeaux, France Duration: 24 Jun 2024 → 28 Jun 2024 Conference number: 13 https://gascom2024.sciencesconf.org/resource/page/id/10

Publication series

Name	Electronic proceedings in theoretical computer science
Publisher	Open Publishing Association
Volume	403
ISSN (Electronic)	2075-2180

Conference

Conference	Random Generation of Combinatorial Structures. Polyominoes and Tilings (GASCom 2024)
Abbreviated title	GASCom 2024
Country/Territory	France
City	Bordeaux
Period	24/06/24 → 28/06/24
Internet address	https://gascom2024.sciencesconf.org/resource/page/id/10

Access to Document

10.4204/eptcs.403.7Licence: CC BY

Abram-2024-Power-quotients-of-plactic-GASCom2024-12-CCBY
Copyright © A. Abram, F. Hivert, J. D. Mitchell, J.-C. Novelli, M. Tsalakou This work is licensed under the Creative Commons Attribution License.
Final published version, 220 KBLicence: CC BY

https://cgi.cse.unsw.edu.au/~eptcs/paper.cgi?GASCom2024.7Licence: CC BY

H2020 OPENDREAMKIT: OPENDREAMKIT (partner)
Linton, S. A. (PI) & Konovalov, O. (CoI)
European Commission
1/09/15 → 31/08/19
Project: Standard

Cite this

Abram, A., Hivert, F., Mitchell, J. D., Novelli, J.-C., & Tsalakou, M. (2024). Power quotients of plactic-like monoids. In S. Brlek, & L. Ferrari (Eds.), Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings: Bordeaux, France, 24-28th June 2024 (pp. 12–17). (Electronic proceedings in theoretical computer science; Vol. 403). Open Publishing Association. https://doi.org/10.4204/eptcs.403.7

Abram, Antoine ; Hivert, Florent ; Mitchell, James D. et al. / Power quotients of plactic-like monoids. Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings: Bordeaux, France, 24-28th June 2024. editor / Srečko Brlek ; Luca Ferrari. Open Publishing Association, 2024. pp. 12–17 (Electronic proceedings in theoretical computer science).

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abstract = "In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations aσ(a) = a with σ(a) ≥ 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 a2 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.",

author = "Antoine Abram and Florent Hivert and Mitchell, {James D.} and Jean-Christophe Novelli and Maria Tsalakou",

note = "Funding: Antoine Abram was partially supported by CRSNG BESC D grant. Florent Hivert was partially supported by OpenDreamKit Horizon 2020 ERI (#676541). James D. Mitchell was partially supported by OpenDreamKit Horizon 2020 ERI (#676541). Jean-Christophe Novelli was partially supported by the ANR program CARPLO.; Random Generation of Combinatorial Structures. Polyominoes and Tilings (GASCom 2024), GASCom 2024 ; Conference date: 24-06-2024 Through 28-06-2024",

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Abram, A, Hivert, F, Mitchell, JD, Novelli, J-C & Tsalakou, M 2024, Power quotients of plactic-like monoids. in S Brlek & L Ferrari (eds), Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings: Bordeaux, France, 24-28th June 2024. Electronic proceedings in theoretical computer science, vol. 403, Open Publishing Association, pp. 12–17, Random Generation of Combinatorial Structures. Polyominoes and Tilings (GASCom 2024), Bordeaux, France, 24/06/24. https://doi.org/10.4204/eptcs.403.7

Power quotients of plactic-like monoids. / Abram, Antoine; Hivert, Florent; Mitchell, James D. et al.
Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings: Bordeaux, France, 24-28th June 2024. ed. / Srečko Brlek; Luca Ferrari. Open Publishing Association, 2024. p. 12–17 (Electronic proceedings in theoretical computer science; Vol. 403).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abram A, Hivert F, Mitchell JD, Novelli JC, Tsalakou M. Power quotients of plactic-like monoids. In Brlek S, Ferrari L, editors, Proceedings of the 13th edition of the Conference on random generation of combinatorial structures. Polyominoes and tilings: Bordeaux, France, 24-28th June 2024. Open Publishing Association. 2024. p. 12–17. (Electronic proceedings in theoretical computer science). doi: 10.4204/eptcs.403.7

Power quotients of plactic-like monoids

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