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Glasgow Mathematical Journal
Article . 2005 . Peer-reviewed
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VALUATIONS OF NEAR POLYGONS

Valuations of near polygons
Authors: De Bruyn, Bart; Vandecasteele, Pieter;

VALUATIONS OF NEAR POLYGONS

Abstract

Ein Fast-\(2d\)-gon ist ein ungerichteter Graph ohne Schlingen vom Durchmesser \(d\), so dass zu jeder Ecke \(x\) und zu jedem maximalen clique \(M\) in \(M\) ein zu \(x\) nächster Punkt existiert. Zu jedem Fastpolygon \(\Gamma\) gehört ein partieller linearer Raum \(S\) (er wird ebenfalls Fastpolygon genannt), deren Punkte die Ecken und deren Geraden die maximalen cliques von \(\Gamma\) sind. Ein Unterraum \(X\) von \(S\) heißt geodätisch abgeschlossen, wenn jeder Punkt eines kürzesten Weges zwischen zwei Punkten von \(X\) ebenfalls in \(X\) liegt. Ein Fastpolygon \(S\) heißt dicht, wenn jede Gerade mit mindestens drei Punkten inzidiert und je zwei Punkte, die die Distanz 2 von einander haben, mindestens zwei gemeinsame Nachbarn besitzen. Die Autoren führen für dichte Fastpolygone den Begriff einer Bewertung ein. Die von ihnen studierten Bewertungen (klassische und ovoidale Bewertungen, hybride Bewertungen, Produktbewertungen, Diagonalbewertungen, SDPS-Bewertungen) eines dichten Fastpolygons \(F\) beschreiben die möglichen Relationen zwischen einem Punkt eines dichten Fastpolygons \(S\) und jedem geodätisch abgeschlossenen Fastunterpolygon von \(S\), welches zu \(F\) isomorph ist. Die Verfasser stellen Eigenschaften von Bewertungen vor und sagen im Abstrakt, dass Bewertungen ein wichtiges Werkzeug zur Klassifikation dichter Fastpolygone sind.

Related Organizations
Keywords

Polar geometry, symplectic spaces, orthogonal spaces, Combinatorial structures in finite projective spaces, near polygon, Combinatorial aspects of finite geometries, Generalized quadrangles and generalized polygons in finite geometry, valuations

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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!
21
Average
Top 10%
Top 10%
bronze