Abstract
We consider the set Σ ( R , C ) of all m × n 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 | Σ ( R , C ) | via the solution to a convex optimization problem. We show that if Σ ( R , C ) is sufficiently large, then a random matrix D ∈ Σ ( R , C ) sampled from the uniform probability measure in Σ ( 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.