Abstract
dc:description.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 <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.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1996
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Ellis, Robert B.
- Chair dc:contributor.committeechair
-
- Day, Martin V.
- Committee members dc:contributor.committeemember
-
- Brown, Ezra A.
- Haskell, Peter E.
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-10072005-094842
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/45075