A Combinatorial Lemma for Complex Numbers
Glen Baxter · The Annals of Mathematical Statistics · 1961
Z1 + * * * + Zn X n > 1. We call SO, Si * * *, Sn, * * * a random walk in the plane. The combinatorial lemmas given below are concerned with the convex hull of the random walk. Specifically, every walk So, * , S. (n + 1 points in the plane) determines a smallest closed, convex set containing these points. The boundary of this set is called the (convex) hull2 of SO, * **, Sn. Later, we will be concerned with three properties of the hull of a walk. We list these properties in the form of variables for later reference. Kn: the number of variables Zi, ***, Zn which are line segments in the hull of SO, * * * , Sn,