Addendum to Schrijver's work on minimum permanents

Ian M. Wanless

doi:10.1007/s00493-006-0040-z

Addendum to Schrijver's work on minimum permanents

Ian M. Wanless^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

Let Λ_n^k denote the set of n × n binary matrices which have each row and column sum equal to k. For 2≤k≤n→ ∞ we show that (min_A∈Λnk per A)^1/n is asymptotically equal to (k - 1) ^k-1 k ^2-k . This confirms Conjecture 23 in Minc's catalogue of open problems.

Original language	English
Pages (from-to)	743-745
Number of pages	3
Journal	Combinatorica
Volume	26
Issue number	6
DOIs	https://doi.org/10.1007/s00493-006-0040-z
Publication status	Published - Dec 2006
Externally published	Yes

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title = "Addendum to Schrijver's work on minimum permanents",

abstract = "Let Λnk denote the set of n × n binary matrices which have each row and column sum equal to k. For 2≤k≤n→ ∞ we show that (minA∈Λnk per A)1/n is asymptotically equal to (k - 1) k-1 k 2-k . This confirms Conjecture 23 in Minc's catalogue of open problems.",

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AB - Let Λnk denote the set of n × n binary matrices which have each row and column sum equal to k. For 2≤k≤n→ ∞ we show that (minA∈Λnk per A)1/n is asymptotically equal to (k - 1) k-1 k 2-k . This confirms Conjecture 23 in Minc's catalogue of open problems.

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KW - 05C70

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JO - Combinatorica

JF - Combinatorica

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ER -

Addendum to Schrijver's work on minimum permanents

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