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math.CO2026
The number of realisations of a random graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of realisations, up to isometries, of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove t…
math.CO2026
The -dimensional realisation number of a rigid graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of (complex) realisations of a rigid graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we provide tw…