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

Abstract

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.

19 pages. Minor updates and corrections

References in corpus (3)

• Algebraic and combinatorial structures on pairs of twin binary trees
• Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson--Schensted--Knuth-type correspondence for quasi-ribbon tableaux
• A note on identities in plactic monoids and monoids of upper-triangular tropical matrices

Cited by in corpus (1)

• A note on identities in plactic monoids and monoids of upper-triangular tropical matrices