On sets without tangents in Galois planes of even order

A. Blokhuis; T. Szõnyi; Z. Weiner

doi:10.1023/A:1024192106237

On sets without tangents in Galois planes of even order

A. Blokhuis, T. Szõnyi, Z. Weiner

Mathematics

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

Abstract

A study on sets without tangents in Galois planes of even order is presented. Examples are given for small sets without tangents but having odd lines. It is shown that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2,q), q even, is at least q+1+√q/6 provided that the set is not of even type.

Original language	English
Pages (from-to)	91-98
Journal	Designs, Codes and Cryptography
Volume	29
DOIs	https://doi.org/10.1023/A:1024192106237
Publication status	Published - 2003

Bibliographical note

MR1993158
Proceedings title: Proceedings of the Conference on Finite Geometries (Oberwolfach, 2001)

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10.1023/A:1024192106237

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title = "On sets without tangents in Galois planes of even order",

abstract = "A study on sets without tangents in Galois planes of even order is presented. Examples are given for small sets without tangents but having odd lines. It is shown that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2,q), q even, is at least q+1+√q/6 provided that the set is not of even type.",

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AU - Blokhuis, A.

AU - Szõnyi, T.

AU - Weiner, Z.

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PY - 2003

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N2 - A study on sets without tangents in Galois planes of even order is presented. Examples are given for small sets without tangents but having odd lines. It is shown that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2,q), q even, is at least q+1+√q/6 provided that the set is not of even type.

AB - A study on sets without tangents in Galois planes of even order is presented. Examples are given for small sets without tangents but having odd lines. It is shown that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2,q), q even, is at least q+1+√q/6 provided that the set is not of even type.

U2 - 10.1023/A:1024192106237

DO - 10.1023/A:1024192106237

M3 - Article

SN - 0925-1022

VL - 29

SP - 91

EP - 98

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

ER -

On sets without tangents in Galois planes of even order

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