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Pair-packings and projective planes

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

D. R. Stinson
D. R. Stinson
Affiliation:
Department of Computer Science University of ManitobaWinnipeg, Manitoba R3T 2N2, Canada
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Abstract

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An (n + 1, n2 + n + 1)-packing is a collection of blocks, each of size n + 1, chosen from a set of size n2 + n + 1, such that no pair of points is contained in more than one block. If any two blocks contain a common point, then the packing can be extended to a projective plane of order n, provided the number of blocks is sufficiently large. We study packings which have a pair of disjoint blocks (such a packing clearly cannot be extended to a projective plane of order n). No such packing can contain more than n2 + n/2 blocks. Also, if n is the order of a projective plane, then we can construct such a packing with n2 + 1 blocks.

MSC classification

Secondary: 05B25: Finite geometries 05B40: Packing and covering
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 27 - 38
Copyright
Copyright © Australian Mathematical Society 1984

References

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