10 citations · 24 across the 11 of their papers we have counts for
20 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…
The partial-fractions method for counting solutions to integral linear systems
Matthias Beck
We present a new tool to compute the number $ϕ_\A (\b)$ of integer solutions to the linear system $$ \x \geq 0 \qquad \A \x = \b $$ where the coefficients of $\A$ and $\b$ are inte…
The polynomial part of a restricted partition function related to the Frobenius problem
Matthias Beck, Ira M. Gessel, Takao Komatsu
Given a set of positive integers A = {a_1,...,a_n}, we study the number p_A (t) of nonnegative integer solutions (m_1,...,m_n) to m_1 a_1 + ... m_n a_n = t. We derive an explicit f…
Counting Lattice Points by means of the Residue Theorem
Matthias Beck
We use the residue theorem to derive an expression for the number of lattice oints in a dilated n-dimensional tetrahedron with vertices at lattice points on each coordinate axis an…