Geodesic
A universality theorem for stressable graphs in the plane
Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 137-148.

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Universality theorems (in the sense of N. Mnëv) claim that the realization space of a combinatorial object (a point configuration, a hyperplane arrangement, a convex polytope, etc.) can be arbitrarily complicated. In the paper, we prove a universality theorem for a graph in the plane with a prescribed oriented matroid of stresses, that is the collection of signs of all possible equilibrium stresses of the graph.This research is motivated by the Grassmanian stratification (Gelfand, Goresky, MacPherson, Serganova) by thin Schubert cells, and by a recent series of papers on stratifications of configuration spaces of tensegrities (Doray, Karpenkov, Schepers, Servatius).
DOI : 10.26493/1855-3974.641.e06
Keywords: Maxwell-Cremona correspondence, Grassmanian stratification, oriented matroid, equilibrium stress 
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Gaiane Panina. A universality theorem for stressable graphs in the plane. Ars Mathematica Contemporanea, Tome 18 (2020) no. 1, pp. 137-148. doi : 10.26493/1855-3974.641.e06. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.641.e06/

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