A Note on Matching Variables to Equations
arxiv(2024)
摘要
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 has
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 which we believe is the simplest possible proof of this
theorem.
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