The Limiting Distributions of the Coefficients of the q-Derangement Numbers

TL;DR

This paper proves that the coefficients of q-derangement numbers, including type B, follow an asymptotically normal distribution as their size increases.

Contribution

It establishes the asymptotic normality of coefficients for both standard and type B q-derangement numbers, extending previous results.

Findings

Coefficients are asymptotically normal for large n

Results apply to both standard and type B q-derangement numbers

Supports the probabilistic understanding of q-derangement distributions

Abstract

We show that the distribution of the coefficients of the q-derangement numbers is asymptotically normal. We also show that this property holds for the q-derangement numbers of type B.