On Whitney numbers of Dowling lattices

✍ Scribed by Moussa Benoumhani

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 746 KB
• Volume: 159
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00095-e

✦ Synopsis

We give some generating functions, recurrence relations for Whitney numbers of Dowling lattices, an explicit formula for Whitney numbers of the second kind, and other relations.

I. Introduction

A finite poset (L, ~< ) is said to be a lattice if every pair of elements, x, y, has an infimum x A y and a supremum or a join x V y. A finite lattice posesses a least and a greatest element, 0 and 1. We say that y covers x ifx ~< t ~< y implies that t = x or t = y. An atom is an element which covers 0; the rank (or the height) of an element x of L, h(x), is the least upper bound of lengths k of chains 0 < xl < x2 < ..-< xk = x between 0 and x.