Asymptotic Estimates for the Number of Contingency Tables, Integer Flows, and Volumes of Transportation Polytopes

DOI10.1093/imrn/rnn133zbMath1163.15015arXiv0709.3810OpenAlexW2963559326MaRDI QIDQ3613885

Alexander I. Barvinok

Publication date: 16 March 2009

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.3810

zbMATH Keywords

convex optimizationasymptotic estimatecontingency tableinteger flowtransportation polytopenon-negative integer matrices

Mathematics Subject Classification ID

Convex programming (90C25) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Transportation, logistics and supply chain management (90B06) Deterministic network models in operations research (90B10) Positive matrices and their generalizations; cones of matrices (15B48) Matrices of integers (15B36)

Related Items

On the closest point to the origin in transportation polytopes, On the mixing time of the Diaconis-Gangolli random walk on contingency tables over \(\mathbb{Z}/q\mathbb{Z} \), Bounds on Kronecker coefficients via contingency tables, On the number of contingency tables and the independence heuristic, Extended commonality of paths and cycles via Schur convexity, Lower bounds for contingency tables via Lorentzian polynomials, Phase transition in random contingency tables with non-uniform margins, Multi-degree bounds on the Betti numbers of real varieties and semi-algebraic sets and applications, On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries, The number of graphs and a random graph with a given degree sequence, Maximum entropy Gaussian approximations for the number of integer points and volumes of polytopes, An approximation algorithm for counting contingency tables, Matrices with prescribed row and column sums, An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums, Random sampling of contingency tables via probabilistic divide-and-conquer