8 citations · 11 across the 9 of their papers we have counts for
7 papers · 1 filter
A local characterization of quasi-crystal graphs
Alan J. Cain, António Malheiro, Fátima Rodrigues +1
It is provided a local characterization of quasi-crystal graphs, by presenting a set of local axioms, similar to the ones introduced by Stembridge for crystal graphs of simply-lace…
Structure of quasi-crystal graphs and applications to the combinatorics of quasi-symmetric functions
Alan J. Cain, António Malheiro, Fátima Rodrigues +1
Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoi…
Conjugacy in Patience Sorting monoids
Alan J. Cain, António Malheiro, Fábio M. Silva
The cyclic shift graph of a monoid is the graph whose vertices are the elements of the monoid and whose edges connect elements that are cyclic shift related. The Patience Sorting a…
Combinatorics of patience sorting monoids
Alan J. Cain, António Malheiro, Fábio M. Silva
This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from perm…
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…
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…