The completion of the classification of the regular near octagons with thick quads
Bart De Bruyn
Postdoctoral Fellow of the Research Foundation - Flanders B. D. Bruyn ( ) Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium
DOI: 10.1007/s10801-006-9099-2
Abstract
Brouwer and Wilbrink [3] showed the nonexistence of regular near octagons whose parameters s, t 2, t 3 and t satisfy s \geq 2, t 2 \geq 2 and t 3 \neq t 2( t 2+1). Later an arithmetical error was discovered in the proof. Because of this error, the existence problem was still open for the near octagons corresponding with certain values of s, t 2 and t 3. In the present paper, we will also show the nonexistence of these remaining regular near octagons.
Pages: 23–29
Keywords: keywords $(regular)$ near polygon
Full Text: PDF
References
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2. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs. Springer-Verlag, Berlin, 1989.
3. A. E. Brouwer and H. A. Wilbrink, “The structure of near polygons with quads,” Geom. Ded., 14 (1983), 145-176.
4. P. J. Cameron, “Dual polar spaces,” Geom. Dedicata, 12 (1982), 75-86.
5. R. Mathon, “On primitive association schemes with three classes,” preprint.
6. A. Neumaier, “Krein conditions and regular near polygons,” J. Combin. Theory Ser. A, 54 (1990), 201- 209.
7. S. E. Payne and J. A. Thas, Finite Generalized Quadrangles, volume 110 of Research Notes in Mathematics. Pitman, Boston, 1984.
8. S. Shad and E. E. Shult, “The near n-gon geometries,” preprint.
9. E. E. Shult and A. Yanushka, “Near n-gons and line systems,” Geom. Dedicata, 9 (1980), 1-72.