2023/05/12 by Joannes Vermant, Vermant, Joannes, Klara Stokes +1
Biochemistry, Genetics and Molecular Biology · Engineering · #52C25 #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2305.07588
openalex publication_date 2023/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will describe articulated motions of realisations of hypergraphs that uses the terminology of graph of groups, and describe the motions of such a framework using group theory. Our approach allows to model a variety of situations, such as parallel redrawings, scenes, polytopes, realisations of graphs on surfaces, and even unique colourability of graphs. This approach allows a concise description of various dualities in rigidity theory. We also provide a lower bound on the dimension of the infinitesimal motions of such a framework in the special case when the underlying group is a Lie group.