The number of realizations of a Laman graph
Algebraic Geometry
2021-03-18 v2 Computational Geometry
Symbolic Computation
Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1701.05500,
title = {The number of realizations of a Laman graph},
author = {Jose Capco and Matteo Gallet and Georg Grasegger and Christoph Koutschan and Niels Lubbes and Josef Schicho},
journal= {arXiv preprint arXiv:1701.05500},
year = {2021}
}
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36 pages