A Class of Geometric Lattices Based on Finite Groups,
Abstract
In the paper the author describes for any finite group G, a class of finite geometric lattices, here called the partial G-partition lattices, which share a number of the properties of the partition lattices. Following a review of preliminary results on ordered sets and geometric lattices, the lattice (Q sub n)(G) of partial G-partitions of an n-set a geometric lattice of rank n, is defined and its structure investigated. The existence is proven of a Boolean sublattice of modular elements in (Q sub n)(G), implying its supersolvability, and its Mobius function and characteristic polynomial are determined, and it is shown that the Whitney numbers of the partial G-partition lattices satisfy recursions and inverse relations analogous to those of the Stirling numbers.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1972
- Accession Number
- AD0746316
Entities
People
- Thomas A. Dowling
Organizations
- University of North Carolina at Chapel Hill