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Some results on defining sets of t-designs

Published online by Cambridge University Press:  17 April 2009

Brenton D. Gray  and
Colin Ramsay
Brenton D. Gray
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia e-mail: [email protected]
Colin Ramsay
Affiliation:
Centre for Discrete Mathematics and Computing, The University of Queensland, Queensland 4072, Australia e-mail: [email protected]
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Abstract

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We investigate how varying the parameters of t-(ν, κ, λ) designs affects the sizes of smallest defining sets. In particular, we consider the effect of varying each of the parameters t, ν and λ. We establish a number of new bounds for the sizes of smallest defining sets and find the size of smallest defining sets for an infinite family of designs. We also show how one of our results can be applied to the problem of finding critical sets of Latin squares.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 203 - 215
Copyright
Copyright © Australian Mathematical Society 1999

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