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Slim Near Polygons

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Abstract

In this paper we initiate the study of hybrid slim near hexagons. These are near hexagons which are not dense and not a generalized hexagon in which each line is incident with exactly three points. In the present paper, we will emphasize slim near hexagons with at least one W(2)-quad or Q(5, 2)-quad. Such near hexagons are finite if there are no special points, i.e. points which lie at distance at most 2 from any other point. We will determine upper bounds for the number of lines through a fixed point. We will also look at the special case where the near hexagon has an order. We will determine all slim near hexagons with an order which contain at least one (necessarily big) Q(5,2)-quad, or at least one big W(2)-quad.

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000, Gent, Belgium

    Bart De Bruyn

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  1. Bart De Bruyn
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Correspondence to Bart De Bruyn.

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AMS Classification 05B25, 51E12

Communicated by: M.J. de Resmini

Postdoctoral Fellow of the Research Foundation–Flanders.

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Bruyn, B.D. Slim Near Polygons. Des Codes Crypt 37, 263–280 (2005). https://doi.org/10.1007/s10623-004-3990-4

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  • DOI: https://doi.org/10.1007/s10623-004-3990-4

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