S. Robins

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20012003

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math.NT2003

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…

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

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…