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Lorentzian polynomials on cones and the Heron-Rota-Welsh conjecture
- Publication Year :
- 2021
-
Abstract
- We give a short proof of the log-concavity of the coefficients of the reduced characteristic polynomial of a matroid. The proof uses an extension of the theory of Lorentzian polynomials to convex cones, and reproves the Hodge-Riemann relations of degree one for the Chow ring of a matroid.
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.00487
- Document Type :
- Working Paper