Journal ArticleDOI
On near-polygons and the coxeter cap in PG(5,3)
TLDR
In this article, an upper bound for the cardinality of a set of points in PG(n, q) with the property that nol of them are contained in a (l− 2)-fiat (n ≥l − 2 ≥ 0) was derived.Abstract:
We find an upper bound for the cardinality of a set of points in PG(n, q) with the property that nol of them are contained in a (l− 2)-fiat (n ≥l − 2 ≥ 0) and we treat the case of equality. We also determine all ovoids and Cameron closed sets of the regular near-hexagon related to the extended ternary Golay code.read more
Citations
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Inequalities for regular near polygons, with applications to m-ovoids
Bart De Bruyn,Frédéric Vanhove +1 more
TL;DR: Two sets of inequalities for regular near polygons are derived and the existence of a 1-ovoid would allow a construction of a strongly regular graph srg(47125,12012,3575,2886), and it is proved that no finite generalized hexagon of order (s,s^3), s>=2, can have1-ovoids.
Journal ArticleDOI
The valuations of the near hexagons related to the Witt designs S(5,6,12) and S(5,8,24)
TL;DR: In this article, Combin et al. showed that if a dense near polygon S contains a hex H isomorphic to 1 or 2, then H is classical in S. The existence of regular near 2d-gons can also be shown with the aid of eigenvalue techniques.
Journal Article
The valuations of the near polygon G n
TL;DR: It is shown that every valuation of the near 2n-gon G(n), n >= 2, is induced by a unique classical valuation ofThe dual polar space DH(2n - 1, 4)into which G( n) is isometrically embeddable.
Recent results on near polygons: a survey
TL;DR: A survey of the most important results regarding near polygons can be found in the Handbook of Incidence Geometry as discussed by the authors, but since the publication several new results concerning these incidence structures were obtained.
Journal ArticleDOI
The hyperplanes of the near hexagon related to the extended ternary Golay code
Bart De Bruyn,Sergey Shpectorov +1 more
TL;DR: In this paper, it was shown that the near hexagon associated with the extended ternary Golay code has, up to isomorphism, 25 hyperplanes and an explicit construction for each of them.
References
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Book
Distance-Regular Graphs
TL;DR: In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.