TY - JOUR

T1 - Embeddability and construction of affine α-resolvable pairwise balanced designs

AU - Bekker, Boris

AU - Ionin, Yury J.

AU - Shrikhande, Mohan S.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

AB - 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.

KW - Affine resolvable symmetric design

KW - Pairwise balanced design

KW - Resolvable

UR - http://www.scopus.com/inward/record.url?scp=84926189545&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1520-6610(1998)6:2<111::AID-JCD3>3.0.CO;2-I

DO - 10.1002/(SICI)1520-6610(1998)6:2<111::AID-JCD3>3.0.CO;2-I

M3 - Article

AN - SCOPUS:84926189545

VL - 6

SP - 111

EP - 129

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 1063-8539

IS - 2

ER -