科研之友
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摘要
We consider two ensembles of 0-1 n x n matrices. The first is the set of all n x n matrices with entries zeroes and ones such that all column sums and all row sums equal r, uniformly weighted. The second is the set of n x n matrices with zero and one entries where the probability that any given entry is one is r/n, the probabilities of the set of individual entries being i. i. d.' s. Calling the two expectation values E and E-B respectively, we develop a formal relation E(perm(A)) = E-B(perm(A))e(Sigma 2) (Ti). (A1) We use two well-known approximating ensembles to E, E-1 and E-2. Replacing E by either E-1 or E-2 we can evaluate all terms in (A1). For either E-1 or E-2 the terms T-i have amazing properties. We conjecture that all these properties hold also for E. We carry through a similar development treating E(perm(m)(A)), with m proportional to n, in place of E(perm(A)).
- 出版日期2017-6
