10 citations · 30 across the 16 of their papers we have counts for
14 papers · 1 filter
Complementary vectors of simplicial complexes
Matt Larson, Alan Stapledon
We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives n…
Lefschetz properties of local face modules
Matt Larson, Alan Stapledon
Local face modules are modules over face rings whose Hilbert function is the local -vector of a triangulation of a simplex. We study when Lefschetz properties hold for local fac…
Differential operators, anisotropy, and simplicial spheres
Kalle Karu, Matt Larson, Alan Stapledon
We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These ident…
Equivariant Ehrhart theory, commutative algebra and invariant triangulations of polytopes
Alan Stapledon
Ehrhart theory is the study of the enumeration of lattice points in lattice polytopes. Equivariant Ehrhart theory is a generalization of Ehrhart theory that takes into account the…
Resolutions of local face modules, functoriality, and vanishing of local -vectors
Matt Larson, Sam Payne, Alan Stapledon
We study the local face modules of triangulations of simplices, i.e., the modules over face rings whose Hilbert functions are local -vectors. In particular, we give resolutions…
Counting lattice points in free sums of polytopes
Alan Stapledon
We show how to compute the Ehrhart polynomial of the free sum of two lattice polytopes containing the origin and in terms of the enumerative combinatorics of and . T…