The unreasonable ubiquitousness of quasi-polynomials

zbMath1300.05031MaRDI QIDQ405135

Kevin M. Woods

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i1p44

zbMATH Keywords

rational generating functionsPresburger arithmeticEhrhart polynomialsquasi-polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) First-order arithmetic and fragments (03F30)

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Cites Work

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• Integer points in polyhedra
• The partial-fractions method for counting solutions to integral linear systems
• On vector partition functions
• The parametric Frobenius problem
• Counting with rational generating functions
• Integer hulls of linear polyhedra and scl in families
• The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959
• Computing the Continuous Discretely
• Points entiers dans les polyèdres convexes
• On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation
• The Unreasonable Effectiveness of Mathematics
• Presburger Arithmetic, Rational Generating Functions, and Quasi-Polynomials
• Generalized Ehrhart polynomials