Title page for ETD etd-10072005-094842


Type of Document Master's Thesis
Author Ellis, Robert B.
URN etd-10072005-094842
Title A Kruskal-Katona theorem for cubical complexes
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Day, Martin V. Committee Chair
Brown, Ezra A. Committee Member
Haskell, Peter E. Committee Member
Keywords
  • cubical
  • simplicial
  • comples
  • Lindstrom
  • Kruskal
Date of Defense 1996-06-06
Availability restricted
Abstract

The optimal number of faces in cubical complexes which lie in cubes refers to the maximum number of faces that can be constructed from a certain number of faces of lower dimension, or the minimum number of faces necessary to construct a certain number of faces of higher dimension. If m is the number of faces of r in a cubical complex, and if s > r(s < r), then the maximum(minimum) number of faces of dimension s that the complex can have is m(s/r) +. (m-m(r/r))(s/r), in terms of upper and lower semipowers. The corresponding formula for simplicial complexes, proved independently by J. B. Kruskal and G. A. Katona, is m(s/r). A proof of the formula for cubical complexes is given in this paper, of which a flawed version appears in a paper by Bernt Lindstrijm. The n-tuples which satisfy the optimaiity conditions for cubical complexes which lie in cubes correspond bijectively with f-vectors of cubical complexes.

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