Generating Function for Pinsky's Combinatorial Second Moment Formula for the Generalized Ulam Problem

Samen Hossein, Shannon Starr

Given a uniform random permutation $\pi \in S_n$, let $Z_{n,k}$ be equal to the number of increasing subsequences of length $k$: so $Z_{n,k}=|\{(i_1,\dots,i_k) \in \mathbb{Z}^k\, :\,…