The minors of matroids with an adjoint
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929725676453888 |
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| author | Grace, Kevin |
| author_facet | Grace, Kevin |
| contents | If $M$ is a matroid, then a simple matroid $M'$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $ϕ$ of the lattice of flats of $M$ into the lattice of flats of $M'$ such that $ϕ$ maps the hyperplanes of $M$ bijectively onto the points of $M'$. In this note, we provide a proof that the class of matroids with an adjoint is minor-closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The minors of matroids with an adjoint Grace, Kevin Combinatorics 05B35 If $M$ is a matroid, then a simple matroid $M'$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $ϕ$ of the lattice of flats of $M$ into the lattice of flats of $M'$ such that $ϕ$ maps the hyperplanes of $M$ bijectively onto the points of $M'$. In this note, we provide a proof that the class of matroids with an adjoint is minor-closed. |
| title | The minors of matroids with an adjoint |
| topic | Combinatorics 05B35 |
| url | https://arxiv.org/abs/2501.17742 |