Polynomials which afford nonnegative, real‐rooted symmetric decompositions have been
investigated recently in algebraic, enumerative and geometric combinatorics. Brändén and …

Wagner (1992) proved that the Hadamard product of two P\'olya frequency sequences that
are interpolated by polynomials is again a P\'olya frequency sequence. We study the …

The Ehrhart quasipolynomial of a rational polytope P encodes the number of integer lattice
points in dilates of P, and the h^* h∗-polynomial of P is the numerator of the accompanying …

The concept of a fully interlacing matrix of formal power series with real coefficients is
introduced. This concept extends and strengthens that of an interlacing sequence of real …

The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by
their number of elements. It has been a challenging open problem to determine which …

The local $ h^* $-polynomial of a lattice polytope is an important invariant arising in Ehrhart
theory. Our focus in this work is on lattice simplices presented in Hermite normal form with a …

We give a combinatorial proof of an identity that involves Eulerian numbers and was
obtained algebraically by Brenti and Welker (2009). To do so, we study alcoved …

The h*-polynomial captures the enumeration of lattice points in dilates of rational polytopes.
For various classes of polytopes, there are many potential properties of this polynomial …

The first part of this dissertation deals with the equivariant Ehrhart theory of the
permutahedron. As a starting point to determining the equivariant Ehrhart theory of the …