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- W4293508440 abstract "Let m,n be positive integers. Define T(m,n) to be the transportation polytope consisting of the m x n non-negative real matrices whose rows each sum to 1 and whose columns each sum to m/n. The special case B(n)=T(n,n) is the much-studied Birkhoff-von Neumann polytope of doubly-stochastic matrices. Using a recent asymptotic enumeration of non-negative integer matrices (Canfield and McKay, 2007), we determine the asymptotic volume of T(m,n) as n goes to infinity, with m=m(n) such that m/n neither decreases nor increases too quickly. In particular, we give an asymptotic formula for the volume of B(n)." @default.
- W4293508440 created "2022-08-30" @default.
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- W4293508440 date "2007-05-16" @default.
- W4293508440 modified "2023-10-16" @default.
- W4293508440 title "The asymptotic volume of the Birkhoff polytope" @default.
- W4293508440 doi "https://doi.org/10.48550/arxiv.0705.2422" @default.
- W4293508440 hasPublicationYear "2007" @default.
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