Geodesic
Counting realizations of Laman graphs on the sphere
Matteo Gallet1 ; Georg Grasegger2 ; Josef Schicho3
1International School for Advanced Studies / Scuola Internazionale Superiore di Studi Avanzati (SISSA)
2Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences
3Research Institute for Symbolic Computation (RISC), JKU University Linz
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space.
DOI : 10.37236/8548
Classification : 05C85, 05C30, 14H10, 51F99, 52C25
Mots-clés : generic minimal rigidity, moduli space, Chow ring, intersection theory

Matteo Gallet  1   ; Georg Grasegger  2   ; Josef Schicho  3

1 International School for Advanced Studies / Scuola Internazionale Superiore di Studi Avanzati (SISSA)
2 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences
3 Research Institute for Symbolic Computation (RISC), JKU University Linz 
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     author = {Matteo Gallet and Georg Grasegger and Josef Schicho},
     title = {Counting realizations of {Laman} graphs on the sphere},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/8548},
     zbl = {1446.05086},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8548/}
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Matteo Gallet; Georg Grasegger; Josef Schicho. Counting realizations of Laman graphs on the sphere. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8548

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