On the number and sizes of double cosets of Sylow subgroups of the symmetric group

Persi Diaconis, Eugenio Giannelli, Robert M. Guralnick +4

Let $P_n$ be a Sylow $p$-subgroup of the symmetric group $S_n$. We investigate the number and sizes of the $P_n\setminus S_n/P_n$ double cosets, showing that most double cosets…