133 citations · 554 across the 117 of their papers we have counts for
7 papers · 1 filter
Convex Hulls of Orbits and Orientations of a Moving Protein Domain
Marco Longinetti, Luca Sgheri, Frank Sottile
We study the facial structure and Carathéodory number of the convex hull of an orbit of the group of rotations in R^3 acting on the space of pairs of anisotropic symmetric 3\times…
Galois groups of Schubert problems via homotopy computation
Anton Leykin, Frank Sottile
Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathem…
A Littlewood-Richardson rule for Grassmannian Permutations
Kevin Purbhoo, Frank Sottile
We give a combinatorial rule for computing intersection numbers on a flag manifold which come from products of Schubert classes pulled back from Grassmannian projections. This rule…
Bounds on the number of real solutions to polynomial equations
Daniel J. Bates, Frédéric Bihan, Frank Sottile
We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the…
Gale duality for complete intersections
Frédéric Bihan, Frank Sottile
We show that every complete intersection of Laurent polynomials in an algebraic torus is isomorphic to a complete intersection of master functions in the complement of a hyperplane…
Linear precision for parametric patches
Luis Garcia-Puente, Frank Sottile
We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the…
On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface
Frederic Bihan, J. Maurice Rojas, Frank Sottile
We show the existence of systems of n polynomial equations in n variables, with a total of n+k+1 distinct monomial terms, possessing [n/k+1]^k nondegenerate positive solutions. (He…