Computing the number of realizations of a Laman graph

Abstract: Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.