Perfect Graeco-Latin balanced incomplete block designs (pergolas)

Rees, D.H. and Preece, Donald A. (1999) Perfect Graeco-Latin balanced incomplete block designs (pergolas). Discrete Mathematics, 198 . pp. 691-712. ISSN 0012-365X. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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A PERfect GraecO-LAtin balanced incomplete block design (PERGOLA) is a block design for two sets of treatments, where (a) each set is arranged relative to the blocks in a balanced incomplete block design (BIBD), (b) each set is arranged relative to the other in a symmetric BIBD, and (c) the overall arrangement is such that there is adjusted orthogonality between the two sets. The currently small literature of pergolas is reviewed, and the topic is shown to be rich in combinatorial interest and unsolved problems. Isomorphism, automorphisms and duality are defined for pergolas, and matters of existence are discussed. A first-ever extensive table of pergolas with r less than or equal to 20 is presented. For each of many of the 66 parameter-sets covered, the Table gives a selection of non-isomorphic pergolas, perhaps based on a selection of non-isomorphic BIBDs for that parameter-set.

Item Type: Article
Uncontrolled keywords: adjusted orthogonality; automorphism groups; cyclic generation; cyclotomy; duals; generalised Kirkman systems; Hadamard designs; isomorphism; self-orthogonal Latin squares; spouse-avoiding mixed-doubles round-robin tournaments; symmetric balanced incomplete block designs
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: F.D. Zabet
Date Deposited: 17 Apr 2009 10:50
Last Modified: 23 Apr 2014 11:19
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