On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series

DOI10.1007/s00209-008-0458-7zbMath1230.05017arXiv0804.3639OpenAlexW2073212241MaRDI QIDQ846887

Matthias Beck, Alan Stapledon

Publication date: 15 February 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3639

zbMATH Keywords

Ehrhart \(\delta \)-polynomialsHilbert series of Veronese subrings of Cohen-Macaulay graded rings.unimodular triangulations of dilations of lattice polytopes

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Cohen-Macaulay modules (13C14)

Related Items

Unimodality questions for integrally closed lattice polytopes, Sums of sets of lattice points and unimodular coverings of polytopes, Laurent polynomials and Eulerian numbers, Unimodality of \(\delta \)-vectors of lattice polytopes and two related properties, Equivariant Ehrhart theory, Commuting Eulerian operators, Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions, Excedance-type polynomials, gamma-positivity and alternatingly increasing property, Combinatorics and Algebra of Geometric Subdivision Operations, Local \(h\)-vectors of quasi-geometric and barycentric subdivisions, On the real-rootedness of the local \(h\)-polynomials of edgewise subdivisions, Simplices for numeral systems, Mixed Ehrhart polynomials, Real-rootedness of variations of Eulerian polynomials, Enumerative \(g\)-theorems for the Veronese construction for formal power series and graded algebras, Interlacing polynomials and the veronese construction for rational formal power series, The Veronese construction for formal power series and graded algebras, Carries, shuffling, and symmetric functions, Log-concavity of asymptotic multigraded Hilbert series, The \(1/k\)-Eulerian polynomials of type \(B\)

Cites Work

• Toroidal embeddings. I
• Some results on Ehrhart polynomials of convex polytopes
• \(f\)-vectors of barycentric subdivisions
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• Lattice points in lattice polytopes
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• Unimodular covers of multiples of polytopes
• On primitive subdivisions of an elementary tetrahedron.
• \(h^\ast\)-vectors, Eulerian polynomials and stable polytopes of graphs
• Inequalities and Ehrhart $\delta $-vectors
• Computing the Continuous Discretely
• Polytopes, Rings, and K-Theory
• Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
• Decompositions of Rational Convex Polytopes
• Hecke operators on rational functions I
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