The Slimmest Geometric Lattices,

Abstract

The Whitney numbers of a finite geometric lattice L of rank r are the numbers Wk of elements of rank k and the coefficients wk of the characteristic polynomial of L, for O < or = k < or = r. Lower bounds are established for the Wk and the absolute values wk(+)=((-1) to the k-th power) wk. The lattices for which equality holds (nontrivially) are described in each case.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1973
Accession Number
ADA042438

Entities

People

  • Richard M. Wilson
  • Thomas A. Dowling

Organizations

  • Ohio State University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boolean Algebra
  • Coefficients
  • Coverings
  • Geometry
  • Graph Theory
  • Identities
  • Inclusions
  • Inequalities
  • Intervals
  • Language
  • Mathematics
  • Polynomials
  • Separators
  • Sequences
  • Topology
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.