Complementary partial resolution squares for Steiner triple systems

In this paper, we introduce a generalization of frames called partial resolution squares. We are interested in constructing sets of complementary partial resolution squares for Steiner triple systems (STS). Our main result is the existence of six complementary partial resolution squares for STS of o...

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Bibliographic Details
Published in:Discrete mathematics 2003-01, Vol.261 (1), p.243-254
Main Authors: Dinitz, J.H., Lamken, E.R., Ling, A.C.H.
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper, we introduce a generalization of frames called partial resolution squares. We are interested in constructing sets of complementary partial resolution squares for Steiner triple systems (STS). Our main result is the existence of six complementary partial resolution squares for STS of order v which can be superimposed in a v× v array so that the resulting array is also the array formed by the superposition of three mutually orthogonal latin squares of order v where v≡1 ( mod 6) , v⩾7, and v∉{55,115,145,205,235,265,319,355,415,493,649,697}.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00471-5