We use Bernstein's Theorem  to obtain combinatorial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume of suitable systems of polynomial equations obtained from the edge length constraints. The bounds can easily be computed and for some classes of graphs, the bounds are tight.
Let g 1 ,. .. , g k be tropical polynomials in n variables with Newton polytopes P 1 ,. .. , P k. We study combinatorial questions on the intersection of the tropical hyper-surfaces defined by g 1 ,. .. , g k , such as the f-vector, the number of unbounded faces and (in case of a curve) the genus. Our point of departure is Vigeland's work  who… (More)