The many aspects of counting lattice points in polytopes
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Publication:2491985
DOI10.1007/s00591-005-0094-9zbMath1093.52006OpenAlexW2071108743MaRDI QIDQ2491985
Publication date: 31 May 2006
Published in: Mathematische Semesterberichte (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00591-005-0094-9
network flowsrational polytopeknapsack problemslattice pointtransportation polytopeBarvinok's algorithmGelfand-Tsetlin patternEhrhart quasipolynomial
Exact enumeration problems, generating functions (05A15) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Lattices and convex bodies (number-theoretic aspects) (11H06) Lattice points in specified regions (11P21)
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Uses Software
Cites Work
- Lattice points in lattice polytopes
- Two poset polytopes
- Pick's theorem and the Todd class of a toric variety
- A lower bound theorem for Ehrhart polynomials of convex polytopes
- The Ehrhart polynomial of a lattice polytope
- Residue formulae for vector partitions and Euler-Maclaurin sums.
- The Ehrhart polynomial of the Birkhoff polytope
- Tensor product multiplicities, canonical and totally positive varieties
- Asymptotics of multivariate sequences. I: Smooth points of the singular variety
- Vertices of Gelfand-Tsetlin polytopes
- Counting integer flows in networks
- The minimum period of the Ehrhart quasi-polynomial of a rational polytope
- Counting lattice points by means of the residue theorem
- A vector partition function for the multiplicities of \(\mathfrak{sl}_k\mathbb C\)
- On vector partition functions
- Combinatorial remarks on partitions of a multipartite number
- Short rational functions for toric algebra and applications
- Effective lattice point counting in rational convex polytopes
- Points entiers dans les polyèdres convexes
- Classification of Quantifier Prefixes Over Diophantine Equations
- The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
- Decompositions of Rational Convex Polytopes
- Lectures on Polytopes
- Sampling contingency tables
- Residue formulae, vector partition functions and lattice points in rational polytopes
- Short rational generating functions for lattice point problems
- The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
- A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
- A Short Proof of Jacobi's Formula for the Number of Representations of an Integer as a Sum of Four Squares
- Polynomials Associated with Finite Gell-Complexes
- On Counting Integral Points in a Convex Rational Polytope
- Precise data locality optimization of nested loops
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