A geometric characterization of dowling lattices

doi:10.1016/0097-3165(91)90032-C

Journal of Combinatorial Theory, Series A

Volume 56, Issue 2, March 1991, Pages 195-202

https://doi.org/10.1016/0097-3165(91)90032-C Get rights and content

Under a Creative Commons license

open archive

Abstract

The Dowling lattices based on finite groups are generalizations of the partition lattices. They form one of the two classes of modularly complemented geometric lattices. In this paper, we present a characterization of the Dowling lattices in terms of the existence of special bases and their weight functions. We show that the hypotheses of this characterization allow us to appeal to a powerful result of Kahn and Kung. A characterization of the partition lattices, Π_n, follows as a corollary of our main result.

Cited by (0)

^∗: Work supported by ONR Contract N00014-88-K-0065.

^†: Current address (effective August 1989): Department of Mathematics, The George Washington University, Washington, D.C. 20052.