Shannon Starr

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20242026

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5 papers · 1 filter

math.CO2026

About the Cramér Large Deviation Property for Bell Polynomials

Sophia Li, Shannon Starr

If $w = (w_{1}, w_{2}, \dots)$ is a sequence in $N = {1, 2, \dots}$ , the partial Bell polynomials based on $w$ are $B_{n, k}$ for $k \in N$ and $…

math.CO2026

Pal's permanent conjecture: proof for block uniform matrices

Andrea Ottolini, Shannon Starr

Consider a symmetric function $C (x, y)$ on $[0, 1] \times [0, 1]$ which is twice continuously differentiable up to the boundary, and which satisfies $ \mathcal{C}(x,y)=\mathca…

math.CO2025

Some Observations about the "Generalized Abundancy Index"

Shannon Starr

Let $A (ℓ, n) \subset S_{n}^{ℓ}$ denote the set of all $ℓ$ -tuples $(π_{1}, \dots, π_{ℓ})$ , for $π_{1}, \dots, π_{ℓ} \in S_{n}$ satisfying: $\forall i < j$ we have $π_iπ_j=…

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 "…