Innovations in Incidence Geometry

1-polarized pseudo-hexagons

Joseph A. Thas and Hendrik van Maldeghem

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Abstract

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 H ( q ) , q even, in PG ( 5 , q ) by intersection numbers with respect to their lines. We prove that, for q 3 , every pseudo-hexagon (i.e. a set of lines of PG ( 5 , q ) with the properties that (1) every plane contains 0 , 1 or q + 1 elements of , (2) every solid contains no more than q 2 + q + 1 and no less than q + 1 elements of , and (3) every point of PG ( 5 , q ) is on q + 1 members of ) which is 1-polarized at some point x (i.e., the lines of through x do not span PG ( 5 , q ) ) is either the line set of the standard embedding of H ( q ) in PG ( 5 , q ) , or q = 2 (in the latter case all pseudo-hexagons are classified in the paper cited).

Article information

Source
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 307-325.

Dates
Received: 21 January 2008
Accepted: 17 March 2008
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323186

Digital Object Identifier
doi:10.2140/iig.2008.6.307

Mathematical Reviews number (MathSciNet)
MR2515274

Zentralblatt MATH identifier
1176.51003

Subjects
Primary: 51E12: Generalized quadrangles, generalized polygons 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

Keywords
generalized hexagons embedding

Citation

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


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References

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