TZAMOS , Charalambos

We address a central question in rigidity theory, namely to bound the number of Euclidean or spherical embeddings of minimally rigid graphs. Since these embeddings correspond to the real roots of certain algebraic systems, the same enumerative question can be asked in complex spaces. Bézout's bound on the quadratic equations that capture the...

Determining the number of solutions of a multi-homogeneous polynomial system is a fundamental problem in algebraic geometry. The multi-homogeneous Bézout (m-Bézout) number bounds from above the number of non-singular solutions of a multi-homogeneous system, but its computation is a #P>-hard problem. Recent work related the m-Bézout number of...