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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