 2329 Paul Federbush
 A Mysterious Cluster Expansion Associated to the Expectation Value
of the Permanent of 01 Matrices (Revised)
(23K, LaTeX)
Apr 23, 23

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Abstract. We consider two ensembles of $n imes n$ matrices. The first is the set of all nxn 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 nxn 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 EB respectively, we develop a formal relation
E(perm(A)) = EB(perm (A)) x exp(sum Ti}.
We also use a wellknown approximating ensemble to E, E1. We prove using E or E1 one obtains the same value of Ti for i < 21. (THE PUBLISHED VERSION OF THIS PAPER ONLY
OBTAINS RESULTS FOR i < 8. We go beyond the results of the published version by taking much more advantage of recent work of Pernici and of Wanless on imatchings on regular bipartite
graphs.) These terms Ti, i < 21, have amazing properties. We conjecture that these properties hold also for all i.
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