## Innovations in Incidence Geometry

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

Antonio Pasini

#### 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 $GF(q)$, $n≥4$, 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
Accepted: 28 October 2007
First available in Project Euclid: 28 February 2019

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

#### 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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