Shannon Starr

activity

20242026

collaborators

Showing 2024Show all

2 papers · 1 filter

math.CO2024

Multifold Convolutions, Generating Functions and 1d Random Walks

Timothy Li, Shannon Starr

We consider multifold convolutions of a combinatorial sequence $(a_{n})_{n = 0}^{\infty}$ : namely, for each $k \in N$ the $k$ -fold convolution is $\mathcal{M}^{(k)}_n(\boldsymbol{a})…

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 "…