On the non-existence of pair covering designs with at least as many points as blocks

Bryant, Darryn, Buchanan, Melinda, Horsley, Daniel, Maenhaut, Barbara and Scharaschkin, Victor (2011) On the non-existence of pair covering designs with at least as many points as blocks. Combinatorica, 31 5: 507-528. doi:10.1007/s00493-011-2639-y

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Author Bryant, Darryn
Buchanan, Melinda
Horsley, Daniel
Maenhaut, Barbara
Scharaschkin, Victor
Title On the non-existence of pair covering designs with at least as many points as blocks
Journal name Combinatorica   Check publisher's open access policy
ISSN 0209-9683
1439-6912
Publication date 2011-11
Sub-type Article (original research)
DOI 10.1007/s00493-011-2639-y
Open Access Status
Volume 31
Issue 5
Start page 507
End page 528
Total pages 22
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2012
Language eng
Formatted abstract
We establish new lower bounds on the pair covering number C λ(υ,k) for infinitely many values of υ, k and λ, including infinitely many values of υ and k for λ = 1. Here, C λ(υ,k) denotes the minimum number of k-subsets of a υ-set of points such that each pair of points occurs in at least λ of the k-subsets. We use these results to prove simple numerical conditions which are both necessary and sufficient for the existence of (K k - e)-designs with more points than blocks.
Keyword Existence
Networks
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 2012 Collection
 
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Created: Sun, 22 Jan 2012, 12:57:53 EST by System User on behalf of School of Mathematics & Physics