10 citations · 30 across the 16 of their papers we have counts for
4 papers · 2 filters
A geometric interpretation of Stanley's monotonicity theorem
Alan Stapledon
We present a new geometric proof of Stanley's monotonicity theorem for lattice polytopes, using an interpretation of -polynomials of lattice polytopes in terms of orbifold Chow…
Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties
Alan Stapledon
We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of th…
On the Log-Concavity of Hilbert Series of Veronese Subrings and Ehrhart Series
Matthias Beck, Alan Stapledon
For every positive integer , consider the linear operator $\U_{n}$ on polynomials of degree at most with integer coefficients defined as follows: if we write $\frac{h(t)}{(1…
Inequalities and Ehrhart -Vectors
Alan Stapledon
For any lattice polytope , we consider an associated polynomial and describe its decomposition into a sum of two polynomials satisfying certain symmetry condition…