5 papers
Characterisations of strong -matroids
Kieran Calvert, Aram Dermenjian, Alex Fink +1
We study characterisations of strong -matroids, compiling a list of five equivalent descriptions. We show a variant of Wenzel's exchange property and the hyperplane exchange pr…
Quadratic exchange equations for Coxeter matroids
Kieran Calvert, Aram Dermenjian, Alex Fink +1
Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each m…
Bruhat Preclosure
Aram Dermenjian
In 2011, Dyer published a series of conjectures on the weak order of Coxeter groups. One of these conjectures stated that the inversion set of the join of two elements in a Coxeter…
Conjugacy Class Growth in Virtually Abelian Groups
Aram Dermenjian, Alex Evetts
We study the conjugacy class growth function in finitely generated virtually abelian groups. That is, the number of elements in the ball of radius in the Cayley graph which int…
Thin MC left regular bands
Aram Dermenjian
We define MC left regular bands and study their adjacency graphs. We prove that for thin MC left regular bands, the adjacency graph is particularly nice and is represented by edge…