Valuated Delta Matroids and Principal Minors of Hermitian matrices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912496514760704 |
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| author | Cheung, Nathan Chin, Tracy Liu, Gaku Vinzant, Cynthia |
| author_facet | Cheung, Nathan Chin, Tracy Liu, Gaku Vinzant, Cynthia |
| contents | In this paper we introduce valuated $Δ$-matroids, a natural generalization of two objects of study in matroid theory: valuated matroids and $Δ$-matroids. We show that these objects exhibit nice properties analogous to ordinary valuated matroids. We also show that these objects arise as the valuations of principal minors of a Hermitian matrix over a valued field, generalizing other forms of $Δ$-matroid representability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Valuated Delta Matroids and Principal Minors of Hermitian matrices Cheung, Nathan Chin, Tracy Liu, Gaku Vinzant, Cynthia Combinatorics Commutative Algebra In this paper we introduce valuated $Δ$-matroids, a natural generalization of two objects of study in matroid theory: valuated matroids and $Δ$-matroids. We show that these objects exhibit nice properties analogous to ordinary valuated matroids. We also show that these objects arise as the valuations of principal minors of a Hermitian matrix over a valued field, generalizing other forms of $Δ$-matroid representability. |
| title | Valuated Delta Matroids and Principal Minors of Hermitian matrices |
| topic | Combinatorics Commutative Algebra |
| url | https://arxiv.org/abs/2507.16275 |