Lattice multipolygons (Q1689611)

In this paper, the authors study the properties of lattice multipolygons, which are certain piecewise linear closed broken lines with vertices in the lattice \(\mathbb Z^2\). They start with a formula on the rotation number of unimodular sequences in \(\mathbb Z^2\). This formula implies the generalized twelve-point theorem of Poonen and Rodriguez-Villegas. The authors state the generalized Pick's formula, and discuss the classification of Ehrhart polynomials of lattice multipolygons and also of several natural subfamilies of lattice multipolygons.