Title: The number of realizations of a Laman graph,
Abstract: Laman graphs model planar frameworks that 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. Such realizations can be seen as
solutions of systems of quadratic equations prescribing the distances between
pairs of points. Using ideas from algebraic and tropical geometry, we provide a
recursive formula for the number of complex solutions of such systems.