On defining sets of full designs

Lefevre, James and Waterhouse, Mary (2010) On defining sets of full designs. Discrete Mathematics, 310 21: 3000-3006. doi:10.1016/j.disc.2010.07.010


Author Lefevre, James
Waterhouse, Mary
Title On defining sets of full designs
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
1872-681X
Publication date 2010-11-06
Sub-type Article (original research)
DOI 10.1016/j.disc.2010.07.010
Volume 310
Issue 21
Start page 3000
End page 3006
Total pages 7
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Collection year 2011
Language eng
Subject C1
0101 Pure Mathematics
Formatted abstract
A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters on a given v-set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {| M | {divides} M is a minimal defining set of D}. The unique simple design with parameters 2 - (v, k, fenced(frac(v - 2, k - 2))) is said to be the full design on v elements; it comprises all possible k-tuples on a v set. We provide two new minimal defining set constructions for full designs with block size k ≥ 3. We then provide a generalisation of the second construction which gives defining sets for all k ≥ 3, with minimality satisfied for k = 3. This provides a significant improvement of the known spectrum for designs with block size three. We hypothesise that this generalisation produces minimal defining sets for all k ≥ 3.
© 2010 Elsevier B.V.
Keyword Defining sets
Full designs
Pairwise balance design
Orthogonal double covers
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
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Created: Sun, 17 Oct 2010, 00:14:18 EST