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On the existence of (3, λ )‐semiframes of type 3 u
Author(s) -
Cao H.
Publication year - 2009
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/jcd.20209
Subject(s) - mathematics , partition (number theory) , combinatorics , disjoint sets , type (biology) , class (philosophy) , discrete mathematics , computer science , artificial intelligence , ecology , biology
A ( k,λ )‐semiframe of type g u is a ( k,λ )‐group‐divisible design of type g u (, , ℬ), in which the collection of blocks ℬ can be written as a disjoint union ℬ=∪ℒ where ℒ is partitioned into parallel classes of and is partitioned into holey parallel classes, each holey parallel class being a partition of \ G j for some G j ∈. In this paper, we shall prove that the necessary conditions for (3, λ )‐semiframes of type 3 u are also sufficient with one exception. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 253–265, 2009