Matthias Beck

activity

20012005

most citedEhrhart-Macdonald reciprocity extended

10 citations · 24 across the 11 of their papers we have counts for

collaborators

Showing 2002Show all

5 papers · 1 filter

math.NT2002

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

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

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

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…