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14 papers
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…
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)
Marcelo Aguiar, Frank Sottile
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determ…
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
Marcelo Aguiar, Frank Sottile
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determ…
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…
Lines Tangent to 2n-2 spheres in R^n
Frank Sottile, Thorsten Theobald
We show that there are 3 \cdot 2^(n-1) complex common tangent lines to 2n-2 general spheres in R^n and that there is a choice of spheres with all common tangents real.
Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials
Frank Sottile
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.