An a-resolvable BIBD is a BIBD with the property that the blocks can be partitioned into disjoint classes such that every class contains each point of the design exactly times. In this paper, we show that the necessary conditions for the existence of -resolvable designs with block size four are suf®
The spectrum of α-resolvable block designs with block size 3
✍ Scribed by D. Jungnickel; R.C. Mullin; S.A. Vanstone
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 517 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
The spectrum of a-resolvable block designs
📜 SIMILAR VOLUMES
Dedicated to Professor Haim Hanani on the occasion of his 75th birthday
## Abstract A group divisible design __GD__(__k__,λ,__t__;__tu__) is α‐resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely α blocks in each class. The necessary conditions for the existence of such a design are λ__t__(__u__ − 1) = __r__(__
## Abstract The necessary conditions for the existence of a super‐simple resolvable balanced incomplete block design on __v__ points with __k__ = 4 and λ = 3, are that __v__ ≥ 8 and __v__ ≡ 0 mod 4. These conditions are shown to be sufficient except for __v__ = 12. © 2003 Wiley Periodicals, Inc.
## Abstract A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. © 2005 Wil
## 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 t