𝔖 Bobbio Scriptorium
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Block designs with large holes and α -resolvable BIBDs

✍ Scribed by Steven C. Furino; Ronald C. Mullin

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
610 KB
Volume
1
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

In a (v, k, λ: w) incomplete block design (IBD) (or PBD [v, {k, w^*^}. λ]), the relation v ≥ (k − 1)w + 1 must hold. In the case of equality, the IBD is referred to as a block design with a large hole, and the existence of such a configuration is equivalent to the existence of a λ‐resolvable BIBD(v − w, k − 1, λ). The existence of such configurations is investigated for the case of k = 5. Necessary and sufficient conditions are given for all v and λ ≢ 2 (mod 4), and for λ ≡ 2 mod 4 with 11 possible exceptions for v. © 1993 John Wiley & Sons, Inc.

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