q-analogues of Ehrhart polynomials

DOI10.1017/S0013091515000243zbMath1343.52012arXiv1301.1844OpenAlexW2963400402MaRDI QIDQ2806119

Frédéric Chapoton

Publication date: 13 May 2016

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.1844

zbMATH Keywords

partially ordered set\(q\)-analogueEhrhart polynomiallattice polytope

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Algebraic aspects of posets (06A11)

Related Items (7)

Effective Poset Inequalities ⋮ Ehrhart tensor polynomials ⋮ Weighted Ehrhart series and a type-\(\mathsf{B}\) analogue of a formula of MacMahon ⋮ On Some Tree-Indexed Series with One and Two Parameters ⋮ On \(q\)-integrals over order polytopes ⋮ Proof of Chapoton's conjecture on Newton polygons of \(q\)-Ehrhart polynomials ⋮ Proof of Chapoton's conjecture on Newton polygons of \(q\)-Ehrhart polynomials

Uses Software

• SageMath
• Sage-Combinat

Cites Work

• \(p\)-partitions revisited
• Two poset polytopes
• On minuscule representations, plane partitions and involutions in complex Lie groups
• Bruhat lattices, plane partition generating functions, and minuscule representations
• \(q\)-Bernoulli numbers and polynomials
• An Elementary View of Euler's Summation Formula
• Computing the Continuous Discretely
• Points entiers dans les polyèdres convexes
• Decompositions of Rational Convex Polytopes
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Combinatorial reciprocity theorems

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