Lower bounds on the number of realizations of rigid graphs
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In this paper we take advantage of a recently published algorithm for computing the number of realizations of minimally rigid graphs. Combining computational results with the theory of constructing new rigid graphs by gluing, we give a new lower bound on the maximal possible number of realizations for graphs with a given number of vertices. We extend these ideas to rigid frameworks in three dimensions and we derive similar lower bounds, by exploiting data from extensive Gröbner basis computations.
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