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math.RA2022
Tropical Representations and Identities of the Stylic Monoid
Thomas Aird, Duarte Ribeiro
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic…
math.RA2021
Identities and bases in the sylvester and Baxter monoids
Alan J. Cain, António Malheiro, Duarte Ribeiro
This paper presents new results on the identities satisfied by the sylvester and Baxter monoids. We show how to embed these monoids, of any rank strictly greater than 2, into a dir…
math.RA2020
Identities and bases in the hypoplactic monoid
Alan J. Cain, António Malheiro, Duarte Ribeiro
This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including in…