Necklaces count polynomial parametric osculants

Abstract We consider the problem of geometrically locally approximating a general complex analytic curve in plane at point by image polynomial parametrization t ? ( x 1 ) , 2 bidegree d . show number such curves is primitive necklaces on white beads and black beads. that this odd when = squarefree use to give partial solution conjecture Rababah. Our results naturally extend generalization regarding hypersurfaces higher dimensions. There, parametrized multidegree … n which optimally osculate given hypersurface are counted with i color i. The proofs these rise numerical homotopy algorithm for computing all osculants point.