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Embeddability and construction of affine α‐resolvable pairwise balanced designs
Author(s) -
Bekker Boris,
Ionin Yury J.,
Shrikhande Mohan S.
Publication year - 1998
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1998)6:2<111::aid-jcd3>3.0.co;2-i
Subject(s) - mathematics , affine transformation , combinatorics , pairwise comparison , partition (number theory) , class (philosophy) , resolution (logic) , discrete mathematics , pure mathematics , statistics , artificial intelligence , computer science
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. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:111–129, 1998