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On the number of matrices and a random matrix with prescribed row and column sums and 0-1 entries
| Content Provider | Semantic Scholar |
|---|---|
| Author | Barvinok, Alexander I. |
| Copyright Year | 2008 |
| Abstract | We consider the set Σ(R,C) of all m×n matrices having 0–1 entries and prescribed row sums R=(r1,…,rm) and column sums C=(c1,…,cn). 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. |
| Starting Page | 316 |
| Ending Page | 339 |
| Page Count | 24 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.aim.2009.12.001 |
| Alternate Webpage(s) | http://www.math.lsa.umich.edu/~barvinok/zeroone.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0806.1480v1.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/0806.1480v3.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0806.1480v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.aim.2009.12.001 |
| Volume Number | 224 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
