Premium
Class‐uniformly resolvable designs with block sizes 2 and 3
Author(s) -
Wevrick D.,
Vanstone S. A.
Publication year - 1996
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(1996)4:3<177::aid-jcd2>3.0.co;2-c
Subject(s) - mathematics , characterization (materials science) , combinatorics , class (philosophy) , block (permutation group theory) , block size , discrete mathematics , computer science , key (lock) , materials science , computer security , artificial intelligence , nanotechnology
In this article we consider restricted resolvable designs (RRP) with block sizes 2 and 3 that are class uniform. A characterization scheme is developed, based on the ratio a : b of pairs to triples, and necessary conditions are provided for the existence of these designs based on this characterization. We show asymptotic existence results when ( a,b ) = (1, 2 n ), n ≥ 1 and when ( a,b ) = (9, 2). We also study the specific cases when ( a,b ) = (1, 2 n ), 1 ≤ n ≤ 5, ( a,b ) = (3, 6 u −2), u ≥ 1 and when ( a,b ) E {(1, 1), (3, 1), (7, 2), (3, 4), (9, 2)}. © 1996 John Wiley & Sons, Inc.