Covers of PG(3,q) and of finite generalized quadrangles

A. Blokhuis; C.M. O'Keefe; S.E. Payne; L. Storme; H.A. Wilbrink

Covers of PG(3,q) and of finite generalized quadrangles

A. Blokhuis, C.M. O'Keefe, S.E. Payne, L. Storme, H.A. Wilbrink

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

5 Citations (Scopus)

Abstract

This article studies covers in PG(3, q) and in generalized quadrangles. The excess of a cover is defined to be the difference between the number of lines in the cover and the number of lines in a spread. In contrast with the theory of partial spreads which tells us that large partial spreads can be extended to spreads, in PG(3, q) and in some generalized quadrangles, there exist minimal covers with small excess. For such minimal covers with small excess, we describe the structure of the set of points lying on at least two lines of the cover.

Original language	English
Pages (from-to)	141-157
Number of pages	17
Journal	Bulletin of the Belgian Mathematical Society : Simon Stevin
Volume	5
Issue number	2-3
Publication status	Published - 1998

Cite this

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AU - Blokhuis, A.

AU - O'Keefe, C.M.

AU - Payne, S.E.

AU - Storme, L.

AU - Wilbrink, H.A.

PY - 1998

Y1 - 1998

N2 - This article studies covers in PG(3, q) and in generalized quadrangles. The excess of a cover is defined to be the difference between the number of lines in the cover and the number of lines in a spread. In contrast with the theory of partial spreads which tells us that large partial spreads can be extended to spreads, in PG(3, q) and in some generalized quadrangles, there exist minimal covers with small excess. For such minimal covers with small excess, we describe the structure of the set of points lying on at least two lines of the cover.

AB - This article studies covers in PG(3, q) and in generalized quadrangles. The excess of a cover is defined to be the difference between the number of lines in the cover and the number of lines in a spread. In contrast with the theory of partial spreads which tells us that large partial spreads can be extended to spreads, in PG(3, q) and in some generalized quadrangles, there exist minimal covers with small excess. For such minimal covers with small excess, we describe the structure of the set of points lying on at least two lines of the cover.

M3 - Article

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JO - Bulletin of the Belgian Mathematical Society : Simon Stevin

JF - Bulletin of the Belgian Mathematical Society : Simon Stevin

IS - 2-3

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Covers of PG(3,q) and of finite generalized quadrangles

Abstract

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