Matthias Beck

activity

20012026

most citedMaximal Periods of (Ehrhart) Quasi-Polynomials

29 citations · 154 across the 72 of their papers we have counts for

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Showing 2002Show all

5 papers · 1 filter

math.NT2002★ 5 cited

An extension of the Frobenius coin-exchange problem

Matthias Beck, Sinai Robins

Given positive integers $a_{1}, ..., a_{n}$ with $g cd (a_{1}, ..., a_{n}) = 1$ , we call an integer t representable if there exist nonnegative integers $m_{1}, ..., m_{n}$ such that $t = m_1 a_1 + ..…

math.NT2002

Some experimental results on the Frobenius problem

Matthias Beck, David Einstein, Shelemyahu Zacks

We study the Frobenius problem: given relatively prime positive integers $a_{1}, ..., a_{d}$ , find the largest value of t (the Frobenius number) such that $\sum_{k = 1}^{d} m_{k} a_{k} = t$ has…

math.NT2002★ 1 cited

The Frobenius problem, rational polytopes, and Fourier-Dedekind Sums

Matthias Beck, Ricardo Diaz, Sinai Robins

We study the number of lattice points in integer dilates of the rational polytope $P = (x_{1}, ..., x_{n}) \in R_{\geq 0}^{n} : \sum_{k = 1}^{n} x_{k} a_{k} \leq 1$ , where $a_{1}, ..., a_{n}$ are posit…

math.CO2002★ 2 cited

The Ehrhart polynomial of the Birkhoff polytope

Matthias Beck, Dennis Pixton

The n'th Birkhoff polytope is the set of all doubly stochastic n-by-n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one…

math.CO2002★ 7 cited

The number of "magic" squares and hypercubes

Matthias Beck, Moshe Cohen, Jessica Cuomo +1

We define a magic square to be a square matrix whose entries are nonnegative integers and whose rows, columns, and main diagonals sum up to the same number. We prove structural res…