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 AbstractThe 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

mis the number of faces ofrin 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.Files

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