A Q-Analog of the Partition Lattice,

Abstract

The report describes for any prime power q a general class of geometric lattices, called q-partition lattices, which share a number of the structural properties of the lattice of partitions of a set. The q-partition lattice is shown to be isomorphic to the lattice of closed sets of a subgeometry of projective geometry over GF(q). The Mobius function and characteristic polynomial are obtained, and an identity and recursion for the Whitney numbers derived. An application is given to the enumeration of factorial designs with no main effects or second order interactions confounded. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1971
Accession Number
AD0734293

Entities

People

  • Thomas A. Dowling

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Factorial Design
  • Geometry
  • Identities
  • Mathematics
  • Projective Geometry
  • Structural Properties

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Theoretical Analysis.