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Exact coverings of triples with specified longest block length

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

R. G. Stanton  and
J. L. Allston
R. G. Stanton
Affiliation:
Department of Computer ScienceUniversity of ManitobaWinnipeg, R3T 2N2, Canada
J. L. Allston
Affiliation:
Department of Computer ScienceUniversity of ManitobaWinnipeg, R3T 2N2, Canada
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Abstract

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A minimal (1,3; ν) covering occurs when we have a family of proper subsets selected from ν elements with the property that every triple occurs exactly once in the family and no family of smaller cardinality possesses this property. Woodall developed a lower bound W for the quantity g(k)(1, 3; ν) which represents the cardinality of a minimal family with longest block of length k. The Woodall bound is only accurate in the region when k ≥ ν/2. We develop an expression for the excess of the true value over the Woodall bound and apply this to show that, when k ≥ ν/2, the value of g(1,3; ν) = W + 1 when k is even and W + 1 + when k is odd.

MSC classification

Secondary: 05B30: Other designs, configurations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 409 - 420
Copyright
Copyright © Australian Mathematical Society 1987

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