$h^\ast $-polynomials of zonotopes

DOI10.1090/tran/7384zbMath1402.05100arXiv1609.08596OpenAlexW2754536801MaRDI QIDQ4644958

Matthias Beck, Katharina Jochemko, Emily McCullough

Publication date: 9 January 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08596

zbMATH Keywords

unimodalityzonotopesEhrhart polynomialsreal-rooted polynomials\(h^\ast\)-polynomialscombinatorial positive valuations

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) Permutations, words, matrices (05A05) Enumeration in graph theory (05C30) Real polynomials: location of zeros (26C10) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Related Items

The Eulerian transformation, Derangements, Ehrhart theory, and local \(h\)-polynomials, Decompositions of Ehrhart \(h^*\)-polynomials for rational polytopes, On the Ehrhart polynomial of minimal matroids, SYMMETRIC DECOMPOSITIONS, TRIANGULATIONS AND REAL‐ROOTEDNESS, Isoperimetric problems for zonotopes, Some results related to Hurwitz stability of combinatorial polynomials, Lattice zonotopes of degree 2, \((M,i)\)-multiset Eulerian polynomials, Partial rank symmetry of distributive lattices for fences, Unimodality of \(\delta \)-vectors of lattice polytopes and two related properties, Commuting Eulerian operators, Some algebraic properties of lecture hall polytopes, Excedance-type polynomials, gamma-positivity and alternatingly increasing property, ARITHMETIC ASPECTS OF SYMMETRIC EDGE POLYTOPES, On the relationship between Ehrhart unimodality and Ehrhart positivity, Pattern-avoiding polytopes, On a rank-unimodality conjecture of Morier-Genoud and Ovsienko, On a rank-unimodality conjecture of Morier-Genoud and Ovsienko, Subdivisions of shellable complexes, Eulerian pairs and Eulerian recurrence systems

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