Given a vector bundle on a smooth projective algebraic variety there exists a unique flag of subbundles (the Harder-Narasimhan filtration). In a paper from 1977, S.S. Shatz associated a polygon to this flag of subbundles and named the polygon the Harder-Narasimhan polygon of the vector bundle. In this talk we will present the bits of combinatorics associated with these polygons. This is joint work with A. Dhillon.