On Minc's sixth conjecture

Ian M. Wanless

doi:10.1080/03081080600562670

On Minc's sixth conjecture

Ian M. Wanless^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let Λ_n^k denote the set of n × n binary matrices which have each row and column sum equal to k. Minc's Conjecture 6 asserts that min_AεΛnk 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 Λ_n^k are proved. The three cases are for matrices which are sufficiently (i) small, (ii) sparse or (iii) dense.

Original language	English
Pages (from-to)	57-63
Number of pages	7
Journal	Linear and Multilinear Algebra
Volume	55
Issue number	1
DOIs	https://doi.org/10.1080/03081080600562670
Publication status	Published - 1 Jan 2007
Externally published	Yes

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title = "On Minc's sixth conjecture",

abstract = "Let Λnk denote the set of n × n binary matrices which have each row and column sum equal to k. Minc's Conjecture 6 asserts that minAεΛnk 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 Λnk are proved. The three cases are for matrices which are sufficiently (i) small, (ii) sparse or (iii) dense.",

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On Minc's sixth conjecture

Abstract

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