On Minc's Sixth Conjecture

Let Λ_n^k denote the set of n×n binary matrices which have each row and column sum k. Minc has conjectured that min{per(A/k) : A in Λ_n^k} is monotone decreasing in k. We prove three special cases of this conjecture and also of the corresponding statement for the maximum permanent in Λ_n^k. The three cases are for matrices which are sufficiently (i) small, (ii) sparse or (iii) dense.

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Last modified: Tue Sep 7 19:10:34 EST 2004