A Note on Matching Variables to Equations
Combinatorics
2024-08-06 v2
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.
Keywords
Cite
@article{arxiv.2401.00724,
title = {A Note on Matching Variables to Equations},
author = {Attila Joó},
journal= {arXiv preprint arXiv:2401.00724},
year = {2024}
}