2020/07/20 by Ahmed Umer Ashraf, Ashraf, Ahmed Umer, Spencer Backman +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #05B35 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Lipid metabolism and biosynthesis
paper · pdf · doi:10.48550/arxiv.2007.10278
openalex publication_date 2020/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lopéz de Medrano-Rinćon-Shaw defined Chern-Schwartz-MacPherson cycles for an arbitrary matroid M and proved by an inductive geometric argument that the unsigned degrees of these cycles agree with the coefficients of T(M;x,0), where T(M;x,y) is the Tutte polynomial associated to M. Ardila-Denham-Huh recently utilized this interpretation of these coefficients in order to demonstrate their log-concavity. In this note we provide a direct calculation of the degree of a matroid Chern-Schwartz-MacPherson cycle by taking its stable intersection with a generic tropical linear space of the appropriate codimension and showing that the weighted point count agrees with the Gioan-Las Vergnas refined activities expansion of the Tutte polynomial.