30 citations · 139 across the 26 of their papers we have counts for
Showing 2016Show all
3 papers · 1 filter
math.CO2016
Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, 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. For certain monoids connected…
math.CO2016★ 4 cited
Identities in plactic, hypoplactic, sylvester, Baxter, and related monoids
Alan J. Cain, António Malheiro
This paper considers whether non-trivial identities are satisfied by certain `plactic-like' monoids that, like the plactic monoid, are closely connected to combinatorics. New resul…
math.CO2016★ 10 cited
Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson--Schensted--Knuth-type correspondence for quasi-ribbon tableaux
Alan J. Cain, António Malheiro
Crystal graphs, in the sense of Kashiwara, carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomorphic components…