A Kruskal-Katona theorem for cubical complexes

Simple item page
dc.contributor.authorEllis, Robert B.en
dc.contributor.committeechairDay, Martin V.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:47:06Zen
dc.date.adate2005-10-07en
dc.date.available2014-03-14T21:47:06Zen
dc.date.issued1996-06-06en
dc.date.rdate2005-10-07en
dc.date.sdate2005-10-07en
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.en
dc.description.degreeMaster of Scienceen
dc.format.extentv, 53 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10072005-094842en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10072005-094842/en
dc.identifier.urihttp://hdl.handle.net/10919/45075en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V855_1996.E455.pdfen
dc.relation.isformatofOCLC# 36268561en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectcubicalen
dc.subjectsimplicialen
dc.subjectcomplesen
dc.subjectLindstromen
dc.subjectKruskalen
dc.subject.lccLD5655.V855 1996.E455en
dc.titleA Kruskal-Katona theorem for cubical complexesen
dc.typeThesisen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LD5655.V855_1996.E455.pdf
Size:
7.03 MB
Format:
Adobe Portable Document Format
Download

Collections

Masters Theses