Foldable Triangulations of Lattice Polygons

TL;DR

This paper presents a simple formula for the signature of foldable triangulations of lattice polygons, which helps establish lower bounds on the real roots of specific polynomial systems called Wronski systems.

Contribution

It introduces a new formula linking the signature of foldable triangulations to boundary properties, advancing understanding of real roots in polynomial systems.

Findings

Derived a simple boundary-based formula for triangulation signatures

Established lower bounds on real roots of Wronski systems

Connected triangulation properties to polynomial root counts

Abstract

We give a simple formula for the signature of a foldable triangulation of a lattice polygon in terms of its boundary. This yields lower bounds on the number of real roots of certain of systems of polynomial equations known as "Wronski systems".