Generic combinatorial rigidity of periodic frameworks

Asimow, 1978, The rigidity of graphs, Trans. Amer. Math. Soc., 245, 279, 10.1090/S0002-9947-1978-0511410-9 Borcea, 2010, Periodic frameworks and flexibility, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466, 2633, 10.1098/rspa.2009.0676 Brylawski, 1986, Constructions, vol. 26, 127 Cormen, 2009 Cox, 2007, Ideals, varieties, and algorithms, 10.1007/978-0-387-35651-8 Jack Edmonds, Gian-Carlo Rota, Submodular set functions (abstract), in: Waterloo Combinatorics Conference, University of Waterloo, Ontario, 1966. Graver, 2001, Counting on frameworks, vol. 25 Laman, 1970, On graphs and rigidity of plane skeletal structures, J. Engrg. Math., 4, 331, 10.1007/BF01534980 Lee, 2008, Pebble game algorithms and sparse graphs, Discrete Math., 308, 1425, 10.1016/j.disc.2007.07.104 Lovász, 1977, Flats in matroids and geometric graphs, 45 Lovász, 2007, 10.1090/chel/361 Lovász, 1982, On generic rigidity in the plane, SIAM J. Algebr. Discrete Methods, 3, 91, 10.1137/0603009 Justin Malestein, Louis Theran, Generic combinatorial rigidity of periodic frameworks, 2010. Preprint, arXiv:1008.1837v2. Maxwell, 1864, On the calculation of the equilibrium and stiffness of frames, Phil. Mag., 10.1080/14786446408643668 Nash-Williams, 1961, Edge-disjoint spanning trees of finite graphs, J. Lond. Math. Soc. (2), 36, 445, 10.1112/jlms/s1-36.1.445 Oxley, 1992 Recski, 1984, A network theory approach to the rigidity of skeletal structures. II. Laman’s theorem and topological formulae, Discrete Appl. Math., 8, 63, 10.1016/0166-218X(84)90079-9 Rivin, 2006, Geometric simulations: a lesson from virtual zeolites, Nat. Mater., 5, 931, 10.1038/nmat1792 Elissa Ross, Periodic rigidity, in: Talk at the Spring AMS Sectional Meeting, 2009. http://www.ams.org/meetings/sectional/1050-52-71.pdf. Elissa Ross, The rigidity of periodic frameworks as graphs on a torus. Ph.D. Thesis, York University, 2011. http://www.math.yorku.ca/~ejross/RossThesis.pdf. Sartbaeva, 2006, The flexibility window in zeolites, Nat. Mater. Streinu, 2010, Slider-pinning rigidity: a Maxwell–Laman-type theorem, Discrete Comput. Geom., 44, 812, 10.1007/s00454-010-9283-y Tay, 1984, Rigidity of multigraphs. I. Linking rigid bodies in n-space, J. Combin. Theory Ser. B, 36, 95, 10.1016/0095-8956(84)90016-9 Treacy, 2004, Enumeration of periodic tetrahedral frameworks. II. polynodal graphs, Microporous Mesoporous Mater., 74, 121, 10.1016/j.micromeso.2004.06.013 Tutte, 1961, On the problem of decomposing a graph into n connected factors, J. London Math. Soc., 36, 221, 10.1112/jlms/s1-36.1.221 Whiteley, 1996, Some matroids from discrete applied geometry, vol. 197, 171 Whiteley, 1988, The union of matroids and the rigidity of frameworks, SIAM J. Discrete Math., 1, 237, 10.1137/0401025 Zaslavsky, 1998, A mathematical bibliography of signed and gain graphs and allied areas, Electron. J. Combin., 5, 124