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Daisy structure in Desarguesian projective planes

Part of: Graph theory Finite geometry and special incidence structures

Published online by Cambridge University Press:  09 April 2009

M. Gabriela Araujo Pardo
M. Gabriela Araujo Pardo
Affiliation:
Instituto de Matemáticas, UNAM Circuito Exterior Ciudad UniversitariaMéxico 04510 D.F.México e-mail: garaujo@math.unam.mx
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Abstract

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We distribute the points and lines of PG(2, 2n+1) according to a special structure that we call the daisy structure. This distribution is intimately related to a special block design which turns out to be isomorphic to PG(n, 2).

We show a blocking set of 3q points in PG(2, 2n+1)that intersects each line in at least two points and we apply this to find a lower bound for the heterochromatic number of the projective plane.

Keywords

Desarguesian projective planeovalhyperovalprojective spacefinite fieldblock designblocking setheterochromatic number.

MSC classification

Secondary: 51E15: Affine and projective planes 51E20: Combinatorial structures in finite projective spaces 51E21: Blocking sets, ovals, $k$-arcs 05C15: Coloring of graphs and hypergraphs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 145 - 154
Copyright
Copyright © Australian Mathematical Society 2003

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