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Mathematics Colloquium

Friday, March 31, 2017 - 15:35 to 16:30
SMS Seminar Hall
Prof. Bart De Bruyn
Ghent University, Belgium
Extremal generalized $2d$-gons

Generalized $2d$-gons are point-line geometries whose incidence graph has diameter $2d$ and girth $4d$. A generalized $2d$-gon is said to have order $(s,t)$ if every line is incident with precisely $s+1$ points and if every point is incident with precisely $t+1$ lines. If $\mathcal{S}$ is a finite generalized $2d$-gon of order $(s,t)$ with $s \not= 1$, then $t \leq s^2$ if $d \in \{ 2,4 \}$ (Higman bounds) and $t \leq s^3$ if $d=3$ (Haemers-Roos bound). In this talk I will discuss old and new combinatorial characterization results for extremal generalized $2d$-gons.

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