A note on regular near polygons

Abstract

Let Gamma be a regular near polygon of order (s, t) with s > 1 and t greater than or equal to 3. Let d be the diameter of Gamma, and let r : = max{i\ (c(i); a(i); b(i)) = (c(1); a(1); b(1))}: In this note we prove several inequalities for Gamma. In particular, we show that s is bounded from above by function in t if d < 3/2 (r + 1). We also consider regular near polygons of order (s, 3).