An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics

DOI10.1007/978-3-319-15081-9_1zbMath1437.52010arXiv1405.7647OpenAlexW4480325MaRDI QIDQ2808002

Felix Breuer

Publication date: 25 May 2016

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7647

zbMATH Keywords

greatest common divisorgenerating functionrational functionpolynomialinteger linear programmingEuclidean algorithmformal power seriesquasipolynomialBarvinok's algorithmquasisymmetric functionsimplicial conecombinatorial reciprocity theorempartial polytopal complexfundamental parallelepiped

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Integer programming (90C10) Linear programming (90C05) Combinatorial aspects of partitions of integers (05A17) Polynomials in number theory (11C08) Polynomials and finite commutative rings (13M10)

Related Items (4)

A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins ⋮ Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts ⋮ Tutte polynomials for regular oriented matroids ⋮ Quasipolynomials and maximal coefficients of Gaussian polynomials

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