ACTA issues

On the number of chords of an affinely regular polygon passing through a given point

Massimo Giulietti

Acta Sci. Math. (Szeged) 74:3-4(2008), 901-913

Abstract. For a point $P$ distinct from the vertices of an affinely regular $d$-gon in the affine plane $AG(2,q)$ with $q$ odd, let $n_P$ denote the number of chords through $P$. The trivial upper bound is $n_P\leq d/2$. In this paper it is shown that this can be improved to $n_P\leq d/3+2$, apart from some exceptional cases described explicitly.

AMS Subject Classification (1991): 51E15, 51E21

Keyword(s): affinely regular polygon, conic, Stöhr-Voloch bound

Received July 20, 2007, and in revised form May 6, 2008, (Registered under 19/2007.)