20 citations · 27 across the 10 of their papers we have counts for
10 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 pro…
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…
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…
Enumerating regions of Shi arrangements per Weyl Cone
Aram Dermenjian, Eleni Tzanaki
Given a Shi arrangement , it is well-known that the total number of regions is counted by the parking number of type and the total number of regions in the domin…
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…
Maximal degree subposets of -Tamari lattices
Aram Dermenjian
In this paper, we study two different subposets of the -Tamari lattice: one in which all elements have maximal in-degree and one in which all elements have maximal out-degree. T…
Sign variation and descents
Nantel Bergeron, Aram Dermenjian, John Machacek
For any and , let be the poset of projective equivalence classes of -vectors of length with sign variation bounded by , ordered by…
The facial weak order on hyperplane arrangements
Aram Dermenjian, Christophe Hohlweg, Thomas McConville +1
We extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all…
The facial weak order and its lattice quotients
Aram Dermenjian, Christophe Hohlweg, Vincent Pilaud
We investigate a poset structure that extends the weak order on a finite Coxeter group to the set of all faces of the permutahedron of . We call this order the facial weak o…