dataset LamanGraphs: The number of realizations of a Laman graph. Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursive formula for the number of complex solutions of such systems.
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References in zbMATH (referenced in 11 articles , 1 standard article )
Showing results 1 to 11 of 11.
- Mc Glue, Ciaran; Stokes, Klara: Generating all rigidity circuits on at most 10 vertices and all Assur graphs on at most 11 vertices (2022)
- Schicho, Josef: And yet it moves: paradoxically moving linkages in kinematics (2022)
- Bartzos, Evangelos; Emiris, Ioannis Z.; Legerský, Jan; Tsigaridas, Elias: On the maximal number of real embeddings of minimally rigid graphs in (\mathbbR^2,\mathbbR^3) and (S^2) (2021)
- Bartzos, Evangelos; Emiris, Ioannis Z.; Schicho, Josef: On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs (2020)
- Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
- Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias: Lower bounds on the number of realizations of rigid graphs (2020)
- Grasegger, Georg; Legerský, Jan; Schicho, Josef: Graphs with flexible labelings allowing injective realizations (2020)
- Bernstein, Daniel I.; Krone, Robert: The tropical Cayley-Menger variety (2019)
- Jackson, Bill; Owen, J. C.: Equivalent realisations of a rigid graph (2019)
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef: The number of realizations of a Laman graph (2018)
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels; Schicho, Josef: Computing the number of realizations of a Laman graph (2017)