Whitney Number Inequalities for Geometric Lattices,

Abstract

Let L be a finite geometric lattice of rank r and for i = 0, 1, ..., r, let W(i) denote the number of elements of L with rank i. For 1 < or = k < or = r - 2, we have W(1) + W(2) + ... + W(k) or = W(r-k) +... + W(r-2) + W(r-1) with equality if and only if the lattice L is modular. We give two further results concerning matchings of lattice elements of rank < or = k into those of rank > or = r - k and observe that a middle term can be interpolated in the above inequality.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1973
Accession Number
ADA042420

Entities

People

  • Richard M. Wilson
  • Thomas A. Dowling

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Coefficients
  • Equations
  • Inequalities
  • Intervals
  • Inversion
  • Linear Algebra
  • Mathematics
  • Observation
  • Permutations
  • Truncation
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematics or Statistics