On The Spectrum of Minimal Defining Sets of Full Designs

Demirkale, Fatih and Yazici, Emine Sule (2014) On The Spectrum of Minimal Defining Sets of Full Designs. Graphs and Combinatorics, 30 1: 141-157. doi:10.1007/s00373-012-1256-x


Author Demirkale, Fatih
Yazici, Emine Sule
Title On The Spectrum of Minimal Defining Sets of Full Designs
Journal name Graphs and Combinatorics   Check publisher's open access policy
ISSN 0911-0119
1435-5914
Publication date 2014-01-01
Year available 2012
Sub-type Article (original research)
DOI 10.1007/s00373-012-1256-x
Volume 30
Issue 1
Start page 141
End page 157
Total pages 17
Place of publication Tokyo, Japan
Publisher Springer
Formatted abstract
A defining set of a t-(v, k, λ) design is a subcollection of the block set of the design which is not contained in any other design with the same parameters. A defining set is said to be minimal if none of its proper subcollections is a defining set. A defining set is said to be smallest if no other defining set has a smaller cardinality. A t-(v, k, λ) design D = (V,B) is called a full design if B is the collection of all possible k-subsets of V. Every simple t-design is contained in a full design and the intersection of a defining set of a full design with a simple t-design contained in it, gives a defining set of the corresponding t-design. With this motivation, in this paper, we study the full designs when t = 2 and k = 3 and we give several families of non-isomorphic minimal defining sets of full designs. Also, it is proven that there exist values in the spectrum of the full design on v elements such that the number of non-isomorphic minimal defining sets on each of these sizes goes to infinity as v→ ∞. Moreover, the lower bound on the size of the defining sets of the full designs is improved by finding the size of the smallest defining sets of the full designs on eight and nine points. Also, all smallest defining sets of the full designs on eight and nine points are classified.
Keyword Defining set spectrum of full designs
Defining sets
Defining sets of combinatorial designs
Defining sets of full designs
Spectrum of minimal defining sets
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online ahead of print 2 November 2012

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 1 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Tue, 31 Dec 2013, 10:19:47 EST by System User on behalf of School of Mathematics & Physics