A note on matching variables to equations
Joó, Attila1
1 Universität Hamburg Mittelweg 177, 20148 Hamburg, Germany
Innovations in Graph Theory, Volume 1 (2024), pp. 33-38.

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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DOI: 10.5802/igt.3
Classification: 15A06, 05B35
Keywords: linear equation system, infinite matroid, thin sum
Joó, Attila 1

1 Universität Hamburg Mittelweg 177, 20148 Hamburg, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Joó, Attila. A note on matching variables to equations. Innovations in Graph Theory, Volume 1 (2024), pp. 33-38. doi : 10.5802/igt.3. https://igt.centre-mersenne.org/articles/10.5802/igt.3/

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