Alan J. Cain

activity

20092023

most citedFinite Gröbner--Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids

30 citations · 132 across the 31 of their papers we have counts for

collaborators

Showing 2014Show all

3 papers · 1 filter

math.GR2014★ 11 cited

Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types $A_{n}$ , $B_{n}$ , $C_{n}$ , $D_{n}$ , and $G_{2}$

Alan J. Cain, Robert D. Gray, António Malheiro

The vertices of any (combinatorial) Kashiwara crystal graph carry a natural monoid structure given by identifying words labelling vertices that appear in the same position of isomo…

math.GR2014

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

Alan J. Cain, Robert Gray, António Malheiro

This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a…

math.GR2014★ 4 cited

Deciding conjugacy in sylvester monoids and other homogeneous monoids

Alan J. Cain, António Malheiro

We give a combinatorial characterization of conjugacy in the sylvester monoid (the monoid of binary search trees), showing that conjugacy is decidable for this monoid. We then prov…

Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types An​, Bn​, Cn​, Dn​, and G2​

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

Deciding conjugacy in sylvester monoids and other homogeneous monoids

Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types $A_{n}$ , $B_{n}$ , $C_{n}$ , $D_{n}$ , and $G_{2}$