Pointwise defining sets and trade cores

Delaney, Cathy, Gray, Brenton D., Gray, Ken, Maenhaut, Barbara M., Sharry, Martin J. and Street, Anne Penfold (1997) Pointwise defining sets and trade cores. Australasian Journal of Combinatorics, 16 51-76.

Author Delaney, Cathy
Gray, Brenton D.
Gray, Ken
Maenhaut, Barbara M.
Sharry, Martin J.
Street, Anne Penfold
Title Pointwise defining sets and trade cores
Journal name Australasian Journal of Combinatorics   Check publisher's open access policy
ISSN 1034-4942
Publication date 1997-09
Sub-type Article (original research)
Volume 16
Start page 51
End page 76
Total pages 26
Place of publication St Lucia, Qld, Australia
Publisher Centre for Discrete Mathematics & Computing
Language eng
Subject 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Abstract A block design D = (V, B) is a set V of v elements together with a set B of b subsets of V called blocks, each containing exactly k elements, such that each element of V occurs in precisely r blocks, for some positive integers rand k. D is called a t-design if every t-subset of V occurs in exactly λt blocks, for some positive integer λt. Such a design D is described as a t-( v, k, λt) design. λ t-( v, k, λt) defining set has previously been defined as a set of blocks which is a subset of a unique t-(v, k, λt) design. A defining set is now more broadly defined to be a set of full and/or partial blocks which is contained in a unique t-( v, k, λt) design. It is a pointwise defining set if partial blocks are present. If only full blocks are present, it may be considered as either a pointwise or a blockwise defining set. The results presented here lead to useful tools for finding both pointwise defining sets of designs, and the relevant generalization of trades. Some examples are given to illustrate this.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Mon, 12 Jul 2010, 10:41:35 EST by Laura McTaggart on behalf of Faculty of Science