Counting Permutations in $S_{2n}$ and $S_{2n+1}$

Yuewen Luo

Let $\alpha (n)$ denote the number of perfect square permutations in the symmetric group $S_n$. The conjecture $\alpha (2n+1)=(2n+1)\alpha (2n)$, provided by Stanley[4], was proved by Blum[1] usi…