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

Citation:
Cain, A. J., and A. Malheiro Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids., Submitted.

Abstract:

This paper considers whether non-trivial identities are satisfied by certain ‘plactic-like’ monoids that, like the plactic monoid, are closely connected with combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga monoids satisfy identities. The existing state of knowledge is discussed for the plactic and Bell monoids.