Complementary partial resolution squares for Steiner triple systems

Authors:
J. H. Dinitz;E. R. Lamken;A. C. H. Ling
Affiliations:
Department of Mathematics and Statistics, University of Vermont, Burlington, VT;Department of Mathematics, 253-37, California Institute of Technology, Pasadena, CA;Department of Computer Science, University of Vermont, Burlington, VT
Venue:
Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
Year:
2003

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Abstract

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}.