Ehrhart polynomials of rank two matroids

DOI10.1016/j.aam.2022.102410zbMath1496.52016arXiv2106.08183OpenAlexW3171183718MaRDI QIDQ2168566

Katharina Jochemko, Luis Ferroni, Benjamin Schröter

Publication date: 31 August 2022

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.08183

zbMATH Keywords

matroidslog-concavitylattice polytopesEhrhart theoryreal-rootednessEhrhart positivity

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Combinatorial aspects of matroids and geometric lattices (05B35) Real polynomials: location of zeros (26C10)

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Ehrhart theory of paving and panhandle matroids ⋮ On the Ehrhart polynomial of Schubert matroids

Cites Work

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• Positroids and Schubert matroids
• Ehrhart series of lecture hall polytopes and Eulerian polynomials for inversion sequences
• Matroid polytopes, nested sets and Bergman fans
• Some results on Ehrhart polynomials of convex polytopes
• Ehrhart polynomials of matroid polytopes and polymatroids
• Common origin of cubic binomial identities: A generalization of Surányi's proof on Le Jen Shoo's formula
• On the Hilbert function of a graded Cohen-Macaulay domain
• Hodge theory for combinatorial geometries
• Combinatorial optimization. Polyhedra and efficiency (3 volumes)
• On lattice path matroid polytopes: integer points and Ehrhart polynomial
• Berline-Vergne valuation and generalized permutohedra
• Matroids are not Ehrhart positive
• Lorentzian polynomials
• Hypersimplices are Ehrhart positive
• Matroids from hypersimplex splits
• On positivity of Ehrhart polynomials
• On the Ehrhart polynomial of minimal matroids
• Unimodality, log-concavity, real-rootedness and beyond
• Unimodality problems in Ehrhart theory
• Inequalities and Ehrhart $\delta $-vectors
• A CHARACTERIZATION OF FACES OF THE BASE POLYHEDRON ASSOCIATED WITH A SUBMODULAR SYSTEM
• Positroids and non-crossing partitions
• Decompositions of Rational Convex Polytopes
• THE HILBERT SERIES OF ALGEBRAS OF THE VERONESE TYPE
• Computing the Continuous Discretely
• An extremal problem for non-separable matroids
• Theory of Matroids
• On the Todd class of the permutohedral variety
• Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity