On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries

Details On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries

2008-06-09

arxiv.org/abs/0806.1480v3

Mathematics

Combinatorics

26 pages, proofs simplified, results strengthened

Scientific paper

We consider the set Sigma(R,C) of all mxn matrices having 0-1 entries and prescribed row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We prove an asymptotic estimate for the cardinality |Sigma(R, C)| via the solution to a convex optimization problem. We show that if Sigma(R, C) is sufficiently large, then a random matrix D in Sigma(R, C) sampled from the uniform probability measure in Sigma(R,C) with high probability is close to a particular matrix Z=Z(R,C) that maximizes the sum of entropies of entries among all matrices with row sums R, column sums C and entries between 0 and 1. Similar results are obtained for 0-1 matrices with prescribed row and column sums and assigned zeros in some positions.

Affiliated with

Also associated with

No associations

Rating

On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries 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 On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-401308