A Note on a Result of Daurat and Nivat

We consider paths in the square lattice and use a valuation called the winding number in order to exhibit some combinatorial properties on these paths. As a corollary, we obtain a characteristic property of self-avoiding closed paths, generalizing in this way a recent result of Daurat and Nivat (2003) on the boundary properties of polyominoes concerning salient and reentrant points.