Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Geometriae Dedicataarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Geometriae Dedicata
Article . 1994 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1994
Data sources: zbMATH Open
versions View all 2 versions
addClaim

Pencils of translation ovals in translation planes

Authors: Glynn, D. G.; Steinke, G. F.;

Pencils of translation ovals in translation planes

Abstract

Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\). An \(i\)-pencil (\(0\leq i\leq 2\)) is a collection of \(i\) lines and \(q+1-i\) translation ovals through a point \(u\) which partition the set of points different from \(u\) which are not in \(I_ \infty\). Pencils in \({\mathcal T}\) can be used to construct new translation planes since pencils correspond to certain spreads. The authors characterize 2-pencils in \(\text{PG} (2,q)\) and describe certain group transitive 1-pencils. The authors leave the investigation of 0-pencils to a forthcoming paper.

Related Organizations
Keywords

spreads, Translation planes and spreads in linear incidence geometry, translation plane, Finite affine and projective planes (geometric aspects), ovals

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    1
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!