Algebraic Combinatorics· 2026Q1
Valuated delta matroids and principal minors of Hermitian matrices
- 1citations
- Q1SCImago
- 2026year
Short summary
Valuated Δ-matroids, a generalization of valuated and Δ-matroids, are introduced and shown to arise from principal minors of Hermitian matrices over valued fields.
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Key points
- Introduced valuated Δ-matroids as a generalization of valuated and Δ-matroids.
- Demonstrated that valuated Δ-matroids share nice properties with ordinary valuated matroids.
- Showed that valuated Δ-matroids arise from principal minors of Hermitian matrices over valued fields.
- Extended existing forms of Δ-matroid representability.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Algebraic Combinatorics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics