Innovations in Incidence Geometry

A characterization of the geometry of large maximal cliques of the alternating forms graph

Antonio Pasini

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Abstract

We prove that the geometry of vertices, edges and qn-cliques of the graph Alt(n+1,q) of (n+1)-dimensional alternating forms over GF(q), n4, is the unique flag-transitive geometry of rank 3 where planes are isomorphic to the point-line system of AG(n,q) and the star of a point is dually isomorphic to a projective space.

Article information

Source
Innov. Incidence Geom., Volume 8, Number 1 (2008), 81-116.

Dates
Received: 15 August 2007
Accepted: 28 October 2007
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323145

Digital Object Identifier
doi:10.2140/iig.2008.8.81

Mathematical Reviews number (MathSciNet)
MR2658660

Zentralblatt MATH identifier
1198.05149

Subjects
Primary: 05E20 05E30: Association schemes, strongly regular graphs 51E24: Buildings and the geometry of diagrams

Keywords
diagram geometry linear-dual-linear geometries distance regular graphs alternating forms graphs

Citation

Pasini, Antonio. A characterization of the geometry of large maximal cliques of the alternating forms graph. Innov. Incidence Geom. 8 (2008), no. 1, 81--116. doi:10.2140/iig.2008.8.81. https://projecteuclid.org/euclid.iig/1551323145


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