3 papers
math.CO2026
An algebraic proof of 1-extension
Alexander Heaton, Martin Winter
We give a new proof that 1-extension preserves generic local rigidity of bar-joint frameworks in all dimensions. The proof does not use a special position argument, which makes the…
math.MG2026
Second-order rigidity of coned polytope frameworks and the stress-flex conjecture from a vector-valued Schläfli formula
Eleni Pachyli, Roman Prosanov, Martin Winter
A coned polytope framework (CPF) is the bar-joint framework obtained from the 1-skeleton of a convex polytope by coning over some interior point. It was recently shown that CPFs ar…
math.CO2024
The Stress-Flex Conjecture
Robert Connelly, Steven J. Gortler, Louis Theran +1
Recently, it has been proven that a tensegrity framework that arises from coning the one-skeleton of a convex polytope is rigid. Since such frameworks are not always infinitesimall…