2024/02/09 by Ayush Kumar Tewari, Tewari, Ayush Kumar
Engineering · Mathematics · #05A15 #05A20 #05B35 #94C05 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2402.06302
openalex publication_date 2024/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We focus on checking the validity of the half-plane property on two prominent classes of transversal matroids, namely lattice path matroids and bicircular matroids. We show that lattice path matroids satisfy the half-plane property. Subsequently, we show an explicit example of a bicircular matroid that is not a positroid and discuss the negative correlation properties of bases of transversal matroids. We prove that sparse paving matroids do not satisfy the Rayleigh property, which helps us gain new perspectives about conjectures on negative correlation in basis elements of matroids in general.