Near polygons with a nice chain of sub-near polygons

Authors:
Bart De Bruyn;Pieter Vandecasteele
Affiliations:
Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium;Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

Citing 3
Cited 6

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On Near Hexagons and Spreads of Generalized Quadrangles

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Two conjectures regarding dense near polygons with three points on each line

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Compatible spreads of symmetry in near polygons

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Dense near polygons with hexes of type HD(5,q2), Q(5,q)×Lq+1 or Q(5,q) ⊗ Q(5,q)

Journal of Combinatorial Theory Series A
A general theory for dense near polygons with a nice chain of subpolygons

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The classification of the slim dense near octagons

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The structure of the spin-embeddings of dual polar spaces and related geometries

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On the order of a non-abelian representation group of a slim dense near hexagon

Journal of Algebraic Combinatorics: An International Journal

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Abstract

In (Eur. J. Combin. 24 (2003) 631) we defined a class of near polygons and conjectured that the near 2n-gons from this class are precisely those near polygons which satisfy the following properties: (i) every line is incident with exactly three points, (ii) every two points at distance 2 have at least two common neighbours, (iii) there exists a chain F0 ⊂ F1 ⊂ ..... ⊂ Fn of geodetically closed sub-near polygons with the property that the sub-near 2i-gon Fi, i ∈ {0,...,n - 1}, is big in the sub-near 2(i + 1)-gon Fi+1. In the present paper we present a proof of this conjecture.