A note on palindromic δ\delta-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart $\delta$-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact.Comment: 4 page

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

A note on palindromic δ-vectors for certain rational polytopes

Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi's Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact

Rational Ehrhart quasi-polynomials

Ehrhart's famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors and it turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.Comment: 15 pages, several changes in the expositio

Periods of Ehrhart Coefficients of Rational Polytopes

Let P⊂R^n be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the number of integer lattice points in the kth dilate of P (k a positive integer) is a quasi-polynomial function of k — that is, a "polynomial" in which the coefficients are themselves periodic functions of k. It is an open problem to determine which quasi-polynomials are the Ehrhart quasi-polynomials of rational polytopes. As partial progress on this problem, we construct families of polytopes in which the periods of the coefficient functions take on various prescribed values