The Perimeter of optimal convex lattice polygons in the sense of different metrics
Miloš Stojaković · Bulletin of the Australian Mathematical Society · 2001
Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric. It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is . for arbitrary ɛ > 0, where . and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.