The world is continuous, but the mind is discrete. David Mumford We seek to bridge some
critical gaps between various? elds of mathematics by studying the interplay between the …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

Many important sequences in combinatorics are known to be log-concave or unimodal, but
many are only conjectured to be so although several techniques using methods from …

Combinatorial reciprocity is a very interesting phenomenon, which can be described as
follows: A polynomial, whose values at positive integers count combinatorial objects of some …

For any lattice polytope $ P $, we consider an associated polynomial $\bar {\delta} _ {P}(t) $
and describe its decomposition into a sum of two polynomials satisfying certain symmetry …

Ehrhart theory is the study of sequences recording the number of integer points in non-
negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is …

This article provides a comprehensive exposition about inequalities that the coefficients of
Ehrhart polynomials and h-polynomials satisfy under various assumptions. We pay …

It is a famous open question whether every integrally closed reflexive polytope has a
unimodal Ehrhart δ-vector. We generalize this question to arbitrary integrally closed lattice …

Ehrhart discovered that the function that counts the number of lattice points in dilations of an
integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart …

We use localization to describe the restriction map from equivariant Chow cohomology to
ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial …