Inherited conics in Hall planes

Aart Blokhuis; István Kovács; Gábor P. Nagy; Tamás Szőnyi

doi:10.1016/j.disc.2018.12.009

Inherited conics in Hall planes

Aart Blokhuis, István Kovács, Gábor P. Nagy (Corresponding author), Tamás Szőnyi

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

2 Downloads (Pure)

Abstract

The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of PG(2,q) remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre–Korchmáros on Desargues configurations with perspective triangles inscribed in a conic.

Original language	English
Pages (from-to)	1098-1107
Number of pages	10
Journal	Discrete Mathematics
Volume	342
Issue number	4
DOIs	https://doi.org/10.1016/j.disc.2018.12.009
Publication status	Published - 1 Apr 2019

Keywords

Arcs
Finite projective planes
Hall planes

Access to Document

10.1016/j.disc.2018.12.009

Cite this

@article{d211b7ea59a14984814bf445f69f9b9e,

title = "Inherited conics in Hall planes",

abstract = "The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of PG(2,q) remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre–Korchm{\'a}ros on Desargues configurations with perspective triangles inscribed in a conic.",

keywords = "Arcs, Finite projective planes, Hall planes",

author = "Aart Blokhuis and Istv{\'a}n Kov{\'a}cs and Nagy, {G{\'a}bor P.} and Tam{\'a}s Sz{\H o}nyi",

year = "2019",

month = apr,

day = "1",

doi = "10.1016/j.disc.2018.12.009",

language = "English",

volume = "342",

pages = "1098--1107",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - Inherited conics in Hall planes

AU - Blokhuis, Aart

AU - Kovács, István

AU - Nagy, Gábor P.

AU - Szőnyi, Tamás

PY - 2019/4/1

Y1 - 2019/4/1

N2 - The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of PG(2,q) remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre–Korchmáros on Desargues configurations with perspective triangles inscribed in a conic.

AB - The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of PG(2,q) remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre–Korchmáros on Desargues configurations with perspective triangles inscribed in a conic.

KW - Arcs

KW - Finite projective planes

KW - Hall planes

UR - http://www.scopus.com/inward/record.url?scp=85059816790&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2018.12.009

DO - 10.1016/j.disc.2018.12.009

M3 - Article

AN - SCOPUS:85059816790

VL - 342

SP - 1098

EP - 1107

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 4

ER -

Inherited conics in Hall planes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this