%0 Journal Article
%T Bounds on generalized Frobenius numbers
%A Lenny Fukshansky
%A Achill Sch¨ırmann
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.ejc.2010.11.001
%X Let $N \geq 2$ and let $1 < a_1 < ... < a_N$ be relatively prime integers. The Frobenius number of this $N$-tuple is defined to be the largest positive integer that has no representation as $\sum_{i=1}^N a_i x_i$ where $x_1,...,x_N$ are non-negative integers. More generally, the $s$-Frobenius number is defined to be the largest positive integer that has precisely $s$ distinct representations like this. We use techniques from the Geometry of Numbers to give upper and lower bounds on the $s$-Frobenius number for any nonnegative integer $s$.
%U http://arxiv.org/abs/1008.4937v3