✦ LIBER ✦
Embeddability and construction of affine α-resolvable pairwise balanced designs
✍ Scribed by Boris Bekker; Yury J. Ionin; Mohan S. Shrikhande
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 315 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
An affine α-resolvable PBD of index λ is a triple (V, B, R), where V is a set (of points), B is a collection of subsets of V (blocks), and R is a partition of B (resolution), satisfying the following conditions: (i) any two points occur together in λ blocks, (ii) any point occurs in α blocks of each resolution class, and (iii) |B| = |V | + |R| -1. Those designs embeddable in symmetric designs are described and two infinite series of embeddable designs are constructed. The analog of the Bruck-Ryser-Chowla theorem for affine α-resolvable PBDs is obtained.