On Minc's Sixth Conjecture

Let Λnk 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 Λnk} is monotone decreasing in k. We prove three special cases of this conjecture and also of the corresponding statement for the maximum permanent in Λnk. 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