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λ-Designs and Related Combinatorial Configurations


Bridges, William Garfield (1969) λ-Designs and Related Combinatorial Configurations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ASAX-G125.


This thesis deals with two problems. The first is the determination of λ-designs, combinatorial configurations which are essentially symmetric block designs with the condition that each subset be of the same cardinality negated. We construct an infinite family of such designs from symmetric block designs and obtain some basic results about their structure. These results enable us to solve the problem for λ = 3 and λ = 4. The second problem deals with configurations related to both λ -designs and (ѵ, k, λ)-configurations. We have (n-1) k-subsets of {1, 2, ..., n}, S1, ..., Sn-1 such that Si ∩ Sj is a λ-set for i ≠ j. We obtain specifically the replication numbers of such a design in terms of n, k, and λ with one exceptional class which we determine explicitly. In certain special cases we settle the problem entirely.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ryser, Herbert J.
Thesis Committee:
  • Unknown, Unknown
Defense Date:17 April 1969
Record Number:CaltechTHESIS:01112016-142041914
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9369
Deposited On:12 Jan 2016 21:29
Last Modified:25 Apr 2024 20:53

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