Work

A note on matching variables to equations

Year: 2024

Type: article

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.

Source: Innovations in Graph Theory

DOI: 10.5802/igt.3

Author: Attila Joó

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Hungarian Scientific Research Fund, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal

Awards: G1357124726, G4576238908, G6164072290, Dualität in der unendlichen Kombinatorik, G6785436599

OpenAlex ID: W4402923910

FWCI:

Cites: 9

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Related to: 10