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The spectrum of α‐resolvable designs with block size four
Author(s) -
Vasiga Troy M. J.,
Furino Steven,
Ling Alan C. H.
Publication year - 2001
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 - 10.1002/1520-6610(2001)9:1<1::aid-jcd1>3.0.co;2-h
Subject(s) - mathematics , disjoint sets , block (permutation group theory) , combinatorics , block size , class (philosophy) , block design , property (philosophy) , point (geometry) , spectrum (functional analysis) , discrete mathematics , computer science , artificial intelligence , key (lock) , philosophy , geometry , computer security , epistemology , physics , quantum mechanics
Abstact: An α‐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 α times. In this paper, we show that the necessary conditions for the existence of α‐resolvable designs with block size four are sufficient, with the exception of (α, ν, λ) = (2, 10, 2). © 2000 John Wiley & Sons, Inc. J Combin Designs 9: 1–16, 2001