Counting realizations of Laman graphs on the sphere

Abstract

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.

arXiv comment15 pages

References in corpus (4)

• Some notes on the equivalence of first-order rigidity in various geometries
• The number of realizations of a Laman graph
• On the maximal number of real embeddings of minimally rigid graphs in ${\mathbb{R}}^2$, ${\mathbb{R}}^3$ and $S^2$
• Compactifications of $M_{0,n}$ associated with Alexander self-dual complexes: Chow ring, $\psi$-classes and intersection numbers

Cited by in corpus (3)

• On the existence of paradoxical motions of generically rigid graphs on the sphere
• A graphical algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero
• The number of realisations of a rigid graph in Euclidean and spherical geometries