Weighted lattice point sums in lattice polytopes, unifying Dehn-Sommerville and Ehrhart-Macdonald

DOI10.1007/s00454-020-00175-2zbMath1462.11082arXiv1805.01504OpenAlexW3003474178MaRDI QIDQ2227237

Evgeny Materov, Matthias Beck, Paul E. Gunnells

Publication date: 10 February 2021

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.01504

zbMATH Keywords

Ehrhart polynomiallattice polytopesEuler-Maclaurin summationDehn-Sommerville relations

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Riemann-Roch theorems (14C40) Lattices and convex bodies (number-theoretic aspects) (11H06) Lattice points in specified regions (11P21)

Cites Work

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• Introduction to Toric Varieties. (AM-131)
• Characteristic Classes of Singular Toric Varieties
• HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
• Lattice points in simple polytopes
• Residue formulae, vector partition functions and lattice points in rational polytopes
• Computing the Continuous Discretely
• Polynomials Associated with Finite Gell-Complexes

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