16 citations · 19 across the 5 of their papers we have counts for
4 papers · 1 filter
Lower bounds for h-vectors of k-CM, independence and broken circuit complexes
Edward Swartz
We present a number of lower bounds for the h-vectors of k-CM, broken circuit and independence complexes. These lead to bounds on the coefficients of the characteristic and reliabi…
Inequalities for the h- and flag h-vectors of geometric lattices
Kathryn Nyman, Ed Swartz
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if D(L) is the order complex of a rank (r+1) geometric lattice L, then for…
g-elements of matroid complexes
Edward Swartz
Let K be the face ring of the independence complex of a matroid. We show that if T is a generic linear system of parameters, then K/T satisfies a weak form of the Hard Lefschetz Th…
Topological representations of matroids
Edward Swartz
There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully par…