By generalising the notion of a unimodular sequence, we create an expression for the winding number of certain ordered sets of lattice points. Since the winding number of the vertices of a Fano polygon is necessarily one, we use this expression as a restriction to classify all Fano polygons without T-singularities and whose singularities in the basket of residual singularities all have equal Gorenstein index.
"Winding number of $r$-modular sequences and applications to the singularity content of a fano polygon." Tohoku Math. J. (2) 73 (1) 137 - 158, 2021. https://doi.org/10.2748/tmj.20200207