Short rational functions for toric algebra and applications

DOI10.1016/j.jsc.2004.02.001zbMath1137.13316arXivmath/0307350OpenAlexW1972231647MaRDI QIDQ2643547

Raymond Hemmecke, Peter Huggins, Ruriko Yoshida, Bernd Sturmfels, Jesús A. De Loera, David C. Haws

Publication date: 24 August 2007

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

Full work available at URL: https://arxiv.org/abs/math/0307350

zbMATH Keywords

Gröbner basislattice pointstoric idealsHilbert seriesEhrhart polynomialBarvinok's algorithmmagic cubes and squaresshort rational function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Exact enumeration problems, generating functions (05A15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

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Uses Software

• LattE

Cites Work

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• The Gröbner fan of an ideal
• Integer programming, Barvinok's counting algorithm and Gomory relaxations.
• Combinatorics and commutative algebra.
• Effective lattice point counting in rational convex polytopes
• Short rational generating functions for lattice point problems
• A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed