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Peer-reviewedCC BY 4.0Algebraic Combinatorics

Valuated delta matroids and principal minors of Hermitian matrices

  • Nathan Cheung1
  • Tracy Chin1
  • Gaku Liu1
  • Cynthia Vinzant1
  1. 1Department of Mathematics, University of Washington, Seattle, Washington, USA
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Abstract

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, or equivalently from maximal isotropic subspaces of a space with Hermitian sesquilinear form, generalizing other forms of Δ -matroid representability.

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Cite

BibTeXRIS
BibTeX
@article{cheung2026valuated,
  title = {{Valuated delta matroids and principal minors of Hermitian matrices}},
  author = {Nathan Cheung and Tracy Chin and Gaku Liu and Cynthia Vinzant},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.512},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.512/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Valuated delta matroids and principal minors of Hermitian matrices
AU  - Nathan Cheung
AU  - Tracy Chin
AU  - Gaku Liu
AU  - Cynthia Vinzant
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.512
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.512/
AB  - 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, or equivalently from maximal isotropic subspaces of a space with Hermitian sesquilinear form, generalizing other forms of Δ -matroid representability.
SN  - 2589-5486
ER  -