Borcea, Ciprian; Streinu, Ileana; Tanigawa, Shin-Ichi Periodic body-and-bar frameworks. (English) Zbl 1329.52020 SIAM J. Discrete Math. 29, No. 1, 93-112 (2015). Summary: Periodic body-and-bar frameworks are abstractions of crystalline structures made of rigid bodies connected by fixed-length bars and subject to the action of a lattice of translations. We give a Maxwell-Laman characterization for minimally rigid periodic body-and-bar frameworks in terms of their quotient graphs. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games. Cited in 5 Documents MSC: 52C25 Rigidity and flexibility of structures (aspects of discrete geometry) 05B35 Combinatorial aspects of matroids and geometric lattices 74E15 Crystalline structure 68W05 Nonnumerical algorithms Keywords:periodic frameworks; rigidity; matroids; crystalline structure PDFBibTeX XMLCite \textit{C. Borcea} et al., SIAM J. Discrete Math. 29, No. 1, 93--112 (2015; Zbl 1329.52020) Full Text: DOI arXiv Link