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Apr 06, 2026
Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T(q3,q) in PG(7,q3)
Abstract
ABSTRACT
In this paper, we study and characterise the natural embedding of the twisted triality hexagon in . We begin by describing the possible intersections of subspaces of with . Then, we provide conditions on a set of lines , which ensure that forms the line set of a naturally embedded twisted triality hexagon. This work follows up on similar results for the split Cayley hexagon by J. A. Thas and H. Van Maldeghem (2008) and F. Ihringer (2014).
In this paper, we study and characterise the natural embedding of the twisted triality hexagon in . We begin by describing the possible intersections of subspaces of with . Then, we provide conditions on a set of lines , which ensure that forms the line set of a naturally embedded twisted triality hexagon. This work follows up on similar results for the split Cayley hexagon by J. A. Thas and H. Van Maldeghem (2008) and F. Ihringer (2014).
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References
11
[1]
Tits J. "Sur La Trialité Et Certain Groupes Qui S'en Déduisent" Publications Mathématiques de l'institut des Hautes Études Scientifiques (1959)
[2]
Van Maldeghem H.1998.Generalized Polygons. volume93.Birkhäuser.
10.1007/978-3-0348-0271-0
[3]
Feit W. "The Nonexistence of Certain Generalized Polygons" Journal of Algebra (1964) 10.1016/0021-8693(64)90028-6
[4]
Thas J. A. "A Characterization of the Natural Embedding of the Split Cayley Hexagon H(q) in PG(6,q) by Intersection Numbers" European Journal of Combinatorics (2008) 10.1016/j.ejc.2007.06.008
[5]
Ihringer F. "A Characterization of the Natural Embedding of the Split Cayley Hexagon in PG(6,q) by Intersection Numbers in Finite Projective Spaces of Arbitrary Dimension" Discrete Mathematics (2014) 10.1016/j.disc.2013.09.012
[6]
Thas J. A. "Flat Lax and Weak Lax Embeddings of Finite Generalized Hexagons" European Journal of Combinatorics (1998) 10.1006/eujc.1998.0240
[7]
Haemers W. "An Inequality for Generalized Hexagons" Geometriae Dedicata (1981) 10.1007/bf01447425
[8]
Ronan M. A. "A Geometric Characterization of Moufang Hexagons" Inventiones Mathematicae (1980) 10.1007/bf01418928
[9]
Offer A. "On the Order of a Generalized Hexagon Admitting an Ovoid or Spread" Journal of Combinatorial Theory, Series A (2002) 10.1006/jcta.2001.3212
[10]
Steinbach A. andH.Van Maldeghem.2004. “Regular Embeddings of Generalized Hexagons.”Canadian Journal of Mathematics56 no.5:1068–1093.
10.4153/cjm-2004-048-3
[11]
Thas J. A. "Polar Spaces, Generalized Hexagons and Perfect Codes" Journal of Combinatorial Theory, Series A (1980) 10.1016/0097-3165(80)90049-7
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Sebastian Petit, Geertrui Van de Voorde (2026). Intersection Numbers of the Natural Embedding of the Twisted Triality Hexagon T(q3,q) in PG(7,q3). Journal of Combinatorial Designs. https://doi.org/10.1002/jcd.70014
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