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≤k≤n→∞ 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−1k^2−k. This confirms Conjecture 23 in Minc's catalogue of open problems.