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.
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