Addendum To Schrijver's Work On Minimum Permanents

Let \( \Lambda ^{k}_{n} \) denote the set of n×n binary matrices which have each row and column sum equal to k. For 2≤kn→∞ we show that \( {\left( {\min _{{A \in \Lambda ^{k}_{n} }} {\text{per}}{\kern 1pt} A} \right)}^{{1/n}} \) is asymptotically equal to (k−1)k−1k2−k. This confirms Conjecture 23 in Minc's catalogue of open problems.

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Correspondence to Ian M. Wanless*.

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* Written while the author was employed by the Department of Computer Science at the Australian National University.

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Wanless*, I.M. Addendum To Schrijver's Work On Minimum Permanents. Combinatorica 26, 743–745 (2006). https://doi.org/10.1007/s00493-006-0040-z

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Mathematics Subject Classification (2000):

  • 15A15
  • 05C80
  • 05C50
  • 05C70