Some results on Whitney numbers of Dowling lattices

TL;DR

This paper investigates properties of Whitney numbers of Dowling lattices, explores their relations with Stirling and Eulerian polynomials, and presents new congruences for Dowling numbers.

Contribution

It introduces new relations between Dowling polynomials and classical polynomials, extending the understanding of their combinatorial properties.

Findings

Established a relation between Stirling and Eulerian polynomials.

Derived new congruences for Dowling numbers.

Explored connections between Dowling polynomials and generalized Eulerian polynomials.

Abstract

In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is relation between Stirling and Eulerian polynomials. Can we find a new relation between Dowling polynomials and other polynomials generalizing Eulerian polynomials? In addition, some congruences for the Dowling numbers are given.