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arXiv · 2401.00724

A Note on Matching Variables to Equations

Attila Joó
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Abstract

We showed with J. P. Gollin that if a (possibly infinite) homogeneous linear equation system has only the trivial solution, then there exists an injective function from the variables to the equations such that each variable appears with non-zero coefficient in its image. Shortly after, a more elementary proof was found by Aharoni and Guo. In this note we present a very short matroid-theoretic proof of this theorem.

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Attila Joó. 2024-08-05. A Note on Matching Variables to Equations. https://arxiv.org/abs/2401.00724

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