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/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.publishersversionpublishe