Samen Hossein

collaborators

2 papers

math.CO2024

About the Moments of the Generalized Ulam Problem

Samen Hossein, Shannon Starr

Given $π \in S_{n}$ , let $Z_{n, k} (π) = \sum_{1 \leq i_{1} < \dots < i_{k} \leq n} 1 ({π_{i_{1}} < \dots < π_{i_{k}}}$ denote the number of increasing subsequences of length $k$ . Consider the "…

math.CO2023

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

Samen Hossein, Shannon Starr

Given a uniform random permutation $π \in S_{n}$ , 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\, :\,…