8 citations · 11 across the 5 of their papers we have counts for
7 papers
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…
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…
A countable family of finitely presented infinite congruence-free monoids
Alan J. Cain, Victor Maltcev, Abdullahi Umar
We prove that monoids are congruence-free for all . This provides a ne…
Unary FA-presentable binary relations: transitivity and classification results
Alan J. Cain, Nik Ruškuc
Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision…