%0 Journal Article
%T Generic Rigidity Matroids with Dilworth Truncations
%A Shin-ichi Tanigawa
%J Mathematics
%D 2010
%I arXiv
%X We prove that the linear matroid that defines generic rigidity of $d$-dimensional body-rod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of ${d+1 \choose 2}$ graphic matroids by applying variants of Dilworth truncation $n_r$ times, where $n_r$ denotes the number of rods. This leads to an alternative proof of Tay's combinatorial characterizations of generic rigidity of rod-bar frameworks and that of identified body-hinge frameworks.
%U http://arxiv.org/abs/1010.5699v2