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 <i>m</i> is the number of faces of <i>r</i> 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<sub>(s/r)</sub> +. (m-m<sub>(r/r)</sub>)<sup>(s/r)</sup>, 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<sup>(s/r)</sup>. 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. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/45075 |
| Date | 07 October 2005 |
| Creators | Ellis, Robert B. |
| Contributors | Mathematics, Day, Martin V., Brown, Ezra A., Haskell, Peter E. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | v, 53 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 36268561, LD5655.V855_1996.E455.pdf |
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