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Convex Cone Conditions on the Structure of Designs


Dukes, Peter James (2003) Convex Cone Conditions on the Structure of Designs. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/V7F7-FQ47.


Various known and original inequalities concerning the structure of combinatorial designs are established using polyhedral cones generated by incidence matrices. This work begins by giving definitions and elementary facts concerning t-designs. A connection with the incidence matrix W of t-subsets versus k-subsets of a finite set is mentioned. The opening chapter also discusses relevant facts about convex geometry (in particular, the Farkas Lemma) and presents an arsenal of binomial identities. The purpose of Chapter 2 is to study the cone generated by columns of W, viewed as an increasing union of cones with certain invariant automorphisms. The two subsequent chapters derive inequalities on block density and intersection patterns in t-designs. Chapter 5 outlines generalizations of W which correspond to hypergraph designs and poset designs. To conclude, an easy consequence of this theory for orthogonal arrays is used in a computing application which generalizes the method of two-point based sampling

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:cone; incidence matrix; orthogonal array; sampling; t-design
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2002. Scott Russell Johnson Prize for Excellence in Graduate Study in Mathematics, 2001.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wilson, Richard M.
Thesis Committee:
  • Wilson, Richard M. (chair)
  • Wales, David B.
  • Ramakrishnan, Dinakar
  • Lorden, Gary A.
Defense Date:30 July 2002
Non-Caltech Author Email:dukes (AT)
Record Number:CaltechETD:etd-07142002-210918
Persistent URL:
Dukes, Peter James0000-0002-5617-083X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2876
Deposited By: Imported from ETD-db
Deposited On:08 Aug 2002
Last Modified:11 Feb 2021 20:17

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