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The ultra log-concavity of Z-polynomials and γ-polynomials of uniform matroids.
- Source :
- Journal of Difference Equations & Applications; Sep2024, Vol. 30 Issue 9, p1370-1384, 15p
- Publication Year :
- 2024
-
Abstract
- Proudfoot, Xu, and Young introduced the Z-polynomial for any matroid and conjectured the polynomial has only real roots. Recently, Ferroni, Nasr, and Vecchi introduced the γ-polynomial of a matroid. In this paper, we prove that both the Z-polynomials and γ-polynomials of uniform matroids are ultra log-concave, which due to Newton's inequality partially supports the real-rootedness conjecture. We also give an alternative formula for the γ-polynomials of uniform matroids. As an application, we use this formula to provide a new proof of the γ-positivity of sparse paving matroids. [ABSTRACT FROM AUTHOR]
- Subjects :
- PAVEMENTS
LOGICAL prediction
POLYNOMIALS
MATROIDS
Subjects
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 30
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 179069914
- Full Text :
- https://doi.org/10.1080/10236198.2024.2351915