8 citations · 11 across the 10 of their papers we have counts for
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math.CO2017
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…
math.GR2017
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…
math.CO2017★ 8 cited
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…