Counting with rational generating functions

DOI10.1016/j.jsc.2007.07.007zbMath1137.05007arXivmath/0504059OpenAlexW2108559011MaRDI QIDQ2474247

Sven Verdoolaege, Kevin M. Woods

Publication date: 5 March 2008

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504059

zbMATH Keywords

rational generating functionsvector partition functionspiecewise quasi-polynomialsparametric polytopesBarvinok algorithmparametric counting functions

Mathematics Subject Classification ID

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

Related Items

Short Presburger Arithmetic Is Hard, On lattice point counting in \(\varDelta\)-modular polyhedra, Presburger Arithmetic, Rational Generating Functions, and Quasi-Polynomials, The unreasonable ubiquitousness of quasi-polynomials, On the number of integer points in translated and expanded polyhedra, INTERMEDIATE SUMS ON POLYHEDRA: COMPUTATION AND REAL EHRHART THEORY, Computation of the highest coefficients of weighted Ehrhart quasi-polynomials of rational polyhedra, Linear recurrence relations in \(q\)-systems via lattice points in polyhedra, COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS, Ehrhart polynomials of matroid polytopes and polymatroids

Uses Software

• LattE

Cites Work

• Counting integer points in parametric polytopes using Barvinok's rational functions
• The partial-fractions method for counting solutions to integral linear systems
• Effective lattice point counting in rational convex polytopes
• Points entiers dans les polyèdres convexes
• Short rational generating functions for lattice point problems
• A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
• A Primal Barvinok Algorithm Based on Irrational Decompositions
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