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.