Rank functions and invariants of delta-matroids

2023/05/01 by Matt Larson, Larson, Matt · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #Combinatorics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Delta #Discrete mathematics #FOS: Mathematics #Function (biology) #Generating function #Mathematics #Matroid #Physics #Rank (graph theory)

paper · pdf · doi:10.48550/arxiv.2305.01008

openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give a rank function axiomatization for delta-matroids and study the corresponding rank generating function. We relate an evaluation of the rank generating function to the number of independent sets of the delta-matroid, and we prove a log-concavity result for that evaluation using the theory of Lorentzian polynomials.

Cited by

• Delta-matroids and toric degenerations in OG(n,2n+1)

Related

• Interlacement and Activities in Delta-Matroids
• Signed permutohedra, delta-matroids, and beyond
• The interlace polynomial of binary delta-matroids and link invariants
• K-classes of delta-matroids and equivariant localization
• Theta rank, levelness, and matroid minors