1 citations · 1 across the 1 of their papers we have counts for
15 papers · 1 filter
General isotropic flags are general (for Grassmannian Schubert calculus)
Frank Sottile
We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert cells defined by such…
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…
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…
Common transversals and tangents to two lines and two quadrics in P^3
Gábor Megyesi, Frank Sottile, Thorsten Theobald
We solve the following geometric problem, which arises in several three-dimensional applications in computational geometry: For which arrangements of two lines and two spheres in R…
Enumerative Real Algebraic Geometry
Frank Sottile
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic ge…