Geodesic
A combinatorial characterization of extremal generalized hexagons
Bart De Bruyn1
1Ghent University
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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A finite generalized $2d$-gon of order $(s,t)$ with $d \in \{ 2,3,4 \}$ and $s \not= 1$ is called extremal if $t$ attains its maximal possible value $s^{e_d}$, where $e_2=e_4=2$ and $e_3=3$. The problem of finding combinatorial conditions that are both necessary and sufficient for a finite generalized $2d$-gon of order $(s,t)$ to be extremal has so far only be solved for the generalized quadrangles. In this paper, we obtain a solution for the generalized hexagons. We also obtain a related combinatorial characterization for extremal regular near hexagons.
DOI : 10.37236/9245
Classification : 51E12
Mots-clés : finite generalized polygons, near hexagons, generalized hexagons

Bart De Bruyn  1

1 Ghent University 
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     title = {A combinatorial characterization of extremal generalized hexagons},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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Bart De Bruyn. A combinatorial characterization of extremal generalized hexagons. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/9245

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