Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids

Supported by an Investigador FCT fellowship (IF/01622/2013/CP1161/CT 0001). This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes), the project PTDC/...

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Bibliographic Details
Main Authors: Cain, Alan J., Malheiro, António
Other Authors: DM - Departamento de Matemática, CMA - Centro de Matemática e Aplicações
Format: Article in Journal/Newspaper
Language:English
Published: 2018
Subjects:
Algebra
Hopf algebra
Rooted trees
Theoretical Computer Science
Geometry and Topology
Computational Theory and Mathematics
Baxter
Patience
taiga
Online Access:http://www.scopus.com/inward/record.url?scp=85053249411&partnerID=8YFLogxK
Description
Summary:Supported by an Investigador FCT fellowship (IF/01622/2013/CP1161/CT 0001). This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes), the project PTDC/MHC-FIL/2583/2014, and the project PTDC/MAT-PUR/31174/2017. This paper considers whether non-trivial identities are satisfied by certain ‘plactic-like’ monoids that, like the plactic monoid, are closely connected to combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga monoids satisfy identities, and indeed give shortest identities satisfied by these monoids. The existing state of knowledge is discussed for the plactic monoid and left and right patience sorting monoids. publishersversion published

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