The nonexistence of regular near octagons with parameters \((s,t,t_2,t_3)=(2,24,0,8)\)
The electronic journal of combinatorics, Tome 17 (2010)
Let $\mathcal{S}$ be a regular near octagon with $s+1=3$ points per line, let $t+1$ denote the constant number of lines through a given point of $\mathcal{S}$ and for every two points $x$ and $y$ at distance $i \in \{ 2,3 \}$ from each other, let $t_i+1$ denote the constant number of lines through $y$ containing a (necessarily unique) point at distance $i-1$ from $x$. It is known, using algebraic combinatorial techniques, that $(t_2,t_3,t)$ must be equal to either $(0,0,1)$, $(0,0,4)$, $(0,3,4)$, $(0,8,24)$, $(1,2,3)$, $(2,6,14)$ or $(4,20,84)$. For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters $(s,t,t_2,t_3)=(2,24,0,8)$ can exist.
@article{10_37236_421,
author = {Bart De Bruyn},
title = {The nonexistence of regular near octagons with parameters \((s,t,t_2,t_3)=(2,24,0,8)\)},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/421},
zbl = {1204.05034},
url = {http://geodesic.mathdoc.fr/articles/10.37236/421/}
}
Bart De Bruyn. The nonexistence of regular near octagons with parameters \((s,t,t_2,t_3)=(2,24,0,8)\). The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/421
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