Mathematics – Combinatorics
Scientific paper
2007-05-16
Mathematics
Combinatorics
4 pages, 1 table
Scientific paper
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).
Canfield Rodney E.
McKay Brendan D.
No associations
LandOfFree
The asymptotic volume of the Birkhoff polytope does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The asymptotic volume of the Birkhoff polytope, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The asymptotic volume of the Birkhoff polytope will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-670768