A discrete Farkas lemma

Details A discrete Farkas lemma A discrete Farkas lemma

2003-03-07

arxiv.org/abs/math/0303094v1

Mathematics

Combinatorics

9 pages; ICCSA 2003 conference, Montreal, May 2003

Scientific paper

Given $A\in \Z^{m\times n}$ and $b\in\Z^m$, we consider the issue of existence of a nonnegative integral solution $x\in \N^n$ to the system of linear equations $Ax=b$. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in $\R^n$ and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.

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