Strictness of the log-concavity of generating polynomials of matroids

DOI10.1016/j.jcta.2020.105351zbMath1464.05035arXiv2003.09568OpenAlexW3129867196MaRDI QIDQ2019614

Satoshi Murai, Akiko Yazawa, Takahiro Nagaoka

Publication date: 21 April 2021

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09568

zbMATH Keywords

independent setmatroidMason's conjectureHodge-Riemann relationLorentzian polynomialmorphism of matroids

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Combinatorial aspects of tropical varieties (14T15) Combinatorial aspects of matroids and geometric lattices (05B35) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (3)

Log-concave poset inequalities (extended abstract) ⋮ Log-concave Gorenstein sequences ⋮ The eigenvalues of the Hessian matrices of the generating functions for trees with \(k\) components

Cites Work

• Unnamed Item
• Sperner property and finite-dimensional Gorenstein algebras associated to matroids
• Homogeneous multivariate polynomials with the half-plane property
• Hodge theory for combinatorial geometries
• Enumeration of points, lines, planes, etc.
• Correlation bounds for fields and matroids
• Logarithmic concavity for morphisms of matroids
• Lorentzian polynomials
• Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials
• On multivariate Newton-like inequalities
• Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid

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