Asymptotic normality of coefficients of some polynomials related to Dowling lattices

Abstract

Recently,

we introduced two sequences of polynomials $(B_n(x,y,z))$ and $(F_n(x,y,z))$,

which unify many familiar polynomials related to Dowling lattices,

such as the Bell polynomials, the Dowling polynomials,

the ordered Bell polynomials, the $r$-Bell polynomials

and the $r$-Dowling polynomials.

In this paper,

we show the asymptotic normality of coefficients of $B_n(x,y,z)$ and $F_n(x,y,z)$.

As applications,

we obtain the asymptotic normality of coefficients of polynomials related to Dowling lattices in a unified approach.