Thin polytopes: Lattice polytopes with vanishing local h^*-polynomial

Keywords

Polytope, Combinatorics, Lattice (music), Mathematics, Polynomial

References

• The Upper Bound Conjecture and Cohen‐Macaulay RingsRichard P. Stanley — 1975
• The decomposition theorem, perverse sheaves and the topology of algebraic mapsMark Andrea A. de Cataldo, Luca Migliorini — 2007
• Multiples of lattice polytopes without interior lattice pointsVictor V. Batyrev, Benjamin Nill — 2006
• Local h-polynomials, invariants of subdivisions, and mixed Ehrhart theoryEric Katz, Alan Stapledon — 2014
• Subdivisions and local h-vectorsRichard P. Stanley — 1992
• Hard Lefschetz theorem for nonrational polytopesKalle Karu — 2001
• Polynomials Associated with Finite Gell-ComplexesI. G. Macdonald — 1971
• A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual DefectAlicia Dickenstein, Benjamin Nill — 2010
• Discriminants, Resultants, and Multidimensional DeterminantsIsrael M. Gelfand, Mikhail Kapranov, Andrei Zelevinsky — 1994
• Lattice points in lattice polytopesU. Betke, Peter McMullen — 1985
• Gorenstein polytopes and their stringy E-functionsBenjamin Nill, Jan Schepers — 2010
• Lower bounds on the coefficients of Ehrhart polynomialsMartin Henk, Makoto Tagami — 2007
• Mini-Workshop: Boundary Value Problems and Spectral GeometryJussi Behrndt, Konstantin Pankrashkin, Olaf Post — 2012
• Lattice polytopes having h*-polynomials with given degree and linear coefficientBenjamin Nill — 2007
• Unimodality Questions for Integrally Closed Lattice PolytopesJan Schepers, Leen Van Langenhoven — 2011
• Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension ThreeGennadiy Averkov, Christian Wagner, Robert Weismantel — 2010
• String cohomology of Calabi–Yau hypersurfaces via mirror symmetryLev Borisov, Anvar R. Mavlyutov — 2001
• Flag subdivisions and γ-vectorsChristos A. Athanasiadis — 2012
• Mirror duality and string-theoretic Hodge numbersVictor V. Batyrev, Lev A. Borisov — 1995
• On empty lattice simplices in dimension 4Margherita Barile, Dominique Bernardi, Alexander Borisov — 2009

Cited by

• Proof of a Conjecture of Batyrev and Juny on Gorenstein PolytopesBenjamin Nill — 2022
• Local h∗[12pt]minimal amsmath wasysym amsfonts amssymb amsbsy mathrsfs upgreek -69pt documenth^*document-polynomials for one-row Hermite normal forEsme Bajo, Benjamin Braun, Giulia Codenotti — 2025
• The number of edges of a symmetric edge polytopeCodenotti, Giulia, Riccardi, Roberto, Venturello, Lorenzo — 2025
• Thin simplices via modular arithmeticVadym Kurylenko — 2024
• Preserving Hodge Vectors of Lattice PolytopesVadym Kurylenko, Benjamin Nill — 2026
• Arnold's monotonicity problemFedor Selyanin — 2020
• Equivariant Ehrhart theory, commutative algebra and invariant triangulations of polytopesAlan Stapledon — 2023
• Newton numbers, vanishing polytopes and algebraic degreesFedor Selyanin — 2025
• On zero-sum polytopes: reciprocity, rigidity, and cyclic sievingDongchun Han, Xuan Wang, Hanbin Zhang — 2026

Related papers

• On the necessity of the invariance conditions for reach control on polytopesMohamed K. Helwa, Zhiyun Lin, Mireille E. Broucke — 2016
• Relaxed in-block controllability of affine systems on polytopesMohamed K. Helwa, Peter E. Caines — 2014
• Uniform decompositions of polytopesDaniel Berend, Luba Bromberg — 2006
• On the computation of viable polytopes for linear systemsYan Gao, John Lygeros — 2003
• Randomly generated polytopes for testing mathematical programming algorithmsW.B. van Dam, J. B. G. Frenk, Jan Telgen — 1983
• Tolerance Analysis With Polytopes in HV-DescriptionSantiago Arroyave-Tobón, Denis Teissandier, Vincent Delos — 2016
• Finding Descriptions of Polytopes via Extended Formulations and LiftingsVolker Kaibel, Andreas Loos — 2011