Asymptotic enumeration of dense 0-1 matrices with specified line sums

Canfield, E. Rodney; Greenhill, Catherine; McKay, Brendan

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Asymptotic enumeration of dense 0-1 matrices with specified line sums

Date

2008

Authors

Canfield, E. Rodney

Greenhill, Catherine

McKay, Brendan

Publisher

Academic Press

Abstract

Let s = (s1, s2, ..., sm) and t = (t1, t2, ..., tn) be vectors of non-negative integers with ∑i = 1m si = ∑j = 1n tj. Let B (s, t) be the number of m × n matrices over {0, 1} with jth row sum equal to sj for 1 ≤ j ≤ m and kth column sum equal to