Shannon Starr

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20242026

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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.NT2026

Asymptotics of the d'Arcais Numbers at Small $k$

Shannon Starr

The d'Arcais numbers are the triangular array ${A (2, n, k) : n = 0, 1, \dots, k = 0, \dots, n}$ , such that $\sum_{n=0}^{\infty} \sum_{k=0}^{n} A(2,n,k) x^k z^n/n! = ((z;z)_{\infty})^…

math.PR2026

Large Deviations for the d'Arcais Numbers

Shannon Starr

The d'Arcais polynomials $P_{n} (z)$ for $n \in {0, 1, \dots}$ are defined as $\sum_{n = 0}^{\infty} P_{n} (z) q^{n} = exp (- z ln ((q; q)_{\infty}))$ where the $q$ -Pochhammer symbol is $(q;q)_{\…

About the Cramér Large Deviation Property for Bell Polynomials

Pal's permanent conjecture: proof for block uniform matrices

Asymptotics of the d'Arcais Numbers at Small k

Large Deviations for the d'Arcais Numbers

Asymptotics of the d'Arcais Numbers at Small $k$