Type: Article

Longest convex lattice chains

Barany, Imre; Roldán-Pensado, Edgardo;

Abstract:

Let T be a triangle with two specified vertices v0,v1?Z2. A convex lattice chain in T from v0 to v1 is defined naturally (see the next paragraph). In this paper we prove what the maximal length of a convex lattice chain is if the area of T is fixed (and large). It is also shown that the solution is unique apart from lattice preserving affine transformations