Innovations in Incidence Geometry
- Innov. Incidence Geom.
- Volume 6-7, Number 1 (2007), 307-325.
In this paper we continue our study begun in “Generalized hexagons and Singer geometries” (2008), aiming at characterizing the embedding of the split Cayley hexagons , even, in by intersection numbers with respect to their lines. We prove that, for , every pseudo-hexagon (i.e. a set of lines of with the properties that (1) every plane contains , or elements of , (2) every solid contains no more than and no less than elements of , and (3) every point of is on members of ) which is 1-polarized at some point (i.e., the lines of through do not span ) is either the line set of the standard embedding of in , or (in the latter case all pseudo-hexagons are classified in the paper cited).
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 307-325.
Received: 21 January 2008
Accepted: 17 March 2008
First available in Project Euclid: 28 February 2019
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Thas, Joseph A.; van Maldeghem, Hendrik. 1-polarized pseudo-hexagons. Innov. Incidence Geom. 6-7 (2007), no. 1, 307--325. doi:10.2140/iig.2008.6.307. https://projecteuclid.org/euclid.iig/1551323186