caa a22 4500 386307393 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198802 xx s 000 0 eng 10.1017/S1446788700031347 doi S1446788700031347 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700031347 The existence of a class of Kirkman squares of index 2 [Elektronische Daten] A Kirkman square with index λ, latinicity μ, block size k and ν points, KSk(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 KSk(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 KS3(ν; 1, 2) for all ν ≡ 3 (mod 12). Copyright © Australian Mathematical Society 1988 05 B 30 nationallicence Lamken E. R. Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N21 3G1, Canada Vanstone S. A. Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N21 3G1, Canada Journal of the Australian Mathematical Society Cambridge University Press 44/1(1988-02), 33-41 1446-7887 44:1<33 1988 44 JAZ https://doi.org/10.1017/S1446788700031347 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700031347 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lamken E. R. Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N21 3G1, Canada NATIONALLICENCE 700 1- Vanstone S. A. Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N21 3G1, Canada NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 44/1(1988-02), 33-41 1446-7887 44:1<33 1988 44 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge