On the Finiteness of Near Polygons with 3 Points on Every Line
Bart De Bruyn
DOI: 10.1023/A:1025165325390
Abstract
Let S be a near polygon of order ( s, t) with quads through every two points at distance 2. The near polygon S is called semifinite if exactly one of s and t is finite. We show that S cannot be semifinite if s = 2 and derive upper bounds for t.
Pages: 41–46
Keywords: near polygon; generalized quadrangle
Full Text: PDF
References
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2. A.E. Brouwer, A.M. Cohen, J.I. Hall, and H.A. Wilbrink, “Near polygons and Fischer spaces,” Geom. Dedicata 49 (1994), 349-368.
3. A.E. Brouwer and H.A. Wilbrink, “The structure of near polygons with quads,” Geom. Dedicata 14 (1983), 145-176.
4. B. De Bruyn and F. De Clerck, “On linear representations of near hexagons,” European J. Combin. 20 (1999), 45-60.
5. P.J. Cameron, “Orbits of permutation groups on ordered sets, II,” J. London Math. Soc. 23(2) (1981), 249-264.
6. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Vol. 110 of Research Notes in Mathematics, Pitman, Boston, 1984.
7. E.E. Shult and A. Yanushka, “Near n-gons and line systems,” Geom. Dedicata 9 (1980), 1-72.
8. J. Tits, “Sur la trialité et certains groupes qui s'en déduisent,” Inst. Hautes Etudes Sci. Publ. Math. 2 (1959), 14-60.