10 citations · 14 across the 4 of their papers we have counts for
4 papers
Ehrhart-Macdonald reciprocity extended
Matthias Beck, Richard Ehrenborg
For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an inti…
Determinations of Analogues of Gauss Sums and Other Trigonometric Sums
Matthias Beck, Bruce C. Berndt, O-Yeat Chan +1
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the…
On Stanley's reciprocity theorem for rational cones
Matthias Beck, Mike Develin
We give a short, self-contained proof of Stanley's reciprocity theorem for a rational cone K \subset R^d. Namely, let sigma_K (x) = sum_{m \in K \cap Z^d} x^m. Then sigma_K (x) and…
Coefficients and Roots of Ehrhart Polynomials
M. Beck, J. A. De Loera, M. Develin +2
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of E…