10 citations · 24 across the 11 of their papers we have counts for
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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…
A Closer Look at Lattice Points in Rational Simplices
Matthias Beck
We generalize Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n+1 rational vertices, we u…
Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube
Matthias Beck, Sinai Robins, Shelemyahu Zacks
Higher-dimensional Dedekind sums are defined as a generalization of a recent 1-dimensional probability model of Dilcher and Girstmair to a d-dimensional cube. The analysis of the f…
The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient
Matthias Beck
We obtain a new motivated proof of the reciprocity law for Dedekind sums by computing the constant coefficient of the Ehrhart polynomial for a rectangular triangle in two ways. On…