A bijective proof of an unusual symmetric group generating function

Mike Zabrocki

For $\sigma \in S_n$, let $D(\sigma )=\{i:{\sigma }_i>{\sigma }_{i+1}\}$ denote the descent set of $\sigma$. The length of the permutation is the number of inversions, denoted by $inv(σ) = \big | \{(i,j) :…