30 citations · 139 across the 26 of their papers we have counts for
5 papers · 1 filter
Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, Baxter, and related monoids
Alan J. Cain, António Malheiro
The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. This paper examines the cycli…
The monoids of the patience sorting algorithm
Alan J. Cain, António Malheiro, Fábio M. Silva
The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences o…
A note on identities in plactic monoids and monoids of upper-triangular tropical matrices
Alan J. Cain, Georg Klein, Łukasz Kubat +2
This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank…
Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids
João Araújo, Michael Kinyon, Janusz Konieczny +1
There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems fo…
Crystals and trees: quasi-Kashiwara operators, monoids of binary trees, and Robinson--Schensted-type correspondences
Alan J. Cain, António Malheiro
Kashiwara's crystal graphs have a natural monoid structure that arises by identifying words labelling vertices that appear in the same position of isomorphic components. The celebr…