In:
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Cambridge University Press (CUP), Vol. 44, No. 1 ( 1988-02), p. 33-41
Abstract:
A Kirkman square with index λ, latinicity μ, block size k and ν points, KS k ( v ; μ, λ), is a t × t array ( t = λ( ν −1)/μ( k − 1)) defined on a ν -set V such that (1) each point of V is contained in precisely μ cells of each row and column, (2) each cell of the array is either empty or contains a k -subset of V , and (3) the collection of blocks obtained from the nonempty cells of the array is a ( ν, k , λ)-BIBD. For μ = 1, the existence of a KS k ( ν ; μ, λ) is equivalent to the existence of a doubly resolvable ( ν, k , λ)-BIBD. In this case the only complete results are for k = 2. The case k = 3, λ = 1 appears to be quite difficult although some existence results are available. For k = 3, λ = 2 the problem seems to be more tractable. In this paper we prove the existence of a KS 3 ( ν ; 1, 2) for all ν ≡ 3 (mod 12).
Type of Medium:
Online Resource
ISSN:
0263-6115
DOI:
10.1017/S1446788700031347
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1988
detail.hit.zdb_id:
2008847-4
detail.hit.zdb_id:
1478743-X
SSG:
17,1
