# 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, JamesWaterhouse, Mary On defining sets of full designs Discrete Mathematics   Check publisher's open access policy 0012-365X1872-681X 2010-11-06 Article (original research) 10.1016/j.disc.2010.07.010 310 21 3000 3006 7 Amsterdam, Netherlands Elsevier 2011 eng C10101 Pure Mathematics 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. Defining setsFull designsPairwise balance designOrthogonal double covers C1 Confirmed Code UQ

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2011 Collection

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