TY - UNPB
T1 - The number of realizations of a Laman graph
AU - Capco, Jose
AU - Grasegger, Georg
AU - Gallet, Matteo
AU - Koutschan, Christoph
AU - Lubbes, Niels
PY - 2017
Y1 - 2017
N2 - 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 recursion formula for the number of complex solutions of such systems.
AB - 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 recursion formula for the number of complex solutions of such systems.
UR - http://www.koutschan.de/data/laman/
M3 - Preprint
T3 - RISC Report Series / Technical report
BT - The number of realizations of a Laman graph
PB - RISC, JKU
CY - Hagenberg, Linz
ER -