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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2401.00724 |
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| _version_ | 1866910553532792832 |
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| author | Joó, Attila |
| author_facet | Joó, Attila |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Matching Variables to Equations Joó, Attila Combinatorics 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. |
| title | A Note on Matching Variables to Equations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.00724 |