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Resolvability of infinite designs

Danziger, Peter; Horsley, Daniel and Webb, Bridget S. (2014). Resolvability of infinite designs. Journal of Combinatorial Theory, Series A, 123(1) pp. 73–85.

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In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t-(v,k,Λ) design with t finite, v infinite and k,λ<v is resolvable and, in fact, has α orthogonal resolutions for each α<v. We also show that, while a t-(v,k,Λ) design with t and λ finite, v infinite and k=v may or may not have a resolution, any resolution of such a design must have v parallel classes containing v blocks and at most λ−1 parallel classes containing fewer than v blocks. Further, a resolution into parallel classes of any specified sizes obeying these conditions is realisable in some design. When k<v and λ=v and when k=v and λ is infinite, we give various examples of resolvable and non-resolvable t-(v,k,Λ) designs.

Item Type: Journal Item
Copyright Holders: 2013 Elsevier Inc.
ISSN: 0097-3165
Keywords: infinite design; parallel class
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 39216
Depositing User: Bridget Webb
Date Deposited: 09 Jan 2014 09:11
Last Modified: 23 May 2019 20:34
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