On collineations and dualities of finite generalized polygons


In this paper we generalize a result of Benson to all finite generalized polygons. In particular, given a collineation θ of a finite generalized polygon S, we obtain a relation between the parameters of S and, for various natural numbers i, the number of points x which are mapped to a point at distance i from x by θ. As a special case we consider generalized 2n-gons of order (1, t) and determine, in the generic case, the exact number of absolute points of a given duality of the underlying generalized n-gon of order t.

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Correspondence to Beukje Temmermans.

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Research supported by the Fund for Scientific Research — Flanders (FWO — Vlaanderen).

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Temmermans, B., Thas, J.A. & Van Maldeghem, H. On collineations and dualities of finite generalized polygons. Combinatorica 29, 569–594 (2009). https://doi.org/10.1007/s00493-009-2435-0

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Mathematics Subject Classification (2000)

  • 51E12