On Minc's sixth conjecture

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Abstract

Let Lambda(k)(n) denote the set of n x n binary matrices which have each row and column sum equal to k. Minc s Conjecture 6 asserts that min(A is an element of Lambda nk) per(1/k)A) is monotone decreasing in k. Here, three special cases of this conjecture and also of the corresponding statement for the maximum permanent in Lambda(k)(n) are proved. The three cases are for matrices which are sufficiently (i) small, (ii) sparse or (iii) dense.
Original languageEnglish
Pages (from-to)57 - 63
Number of pages7
JournalLinear and Multilinear Algebra
Volume55
Issue number1
Publication statusPublished - 2007

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