133 citations · 554 across the 117 of their papers we have counts for
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Toric ideals, real toric varieties, and the algebraic moment map
Frank Sottile
This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real…
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…
Maximally inflected real rational curves
Viatcheslav Kharlamov, Frank Sottile
We introduce and begin the topological study of real rational plane curves, all of whose inflection points are real. The existence of such curves is a corollary of results in the r…
Real k-flats tangent to quadrics in R^n
Frank Sottile, Thorsten Theobald
Let d_{k,n} and #_{k,n} denote the dimension and the degree of the Grassmannian G_{k,n} of k-planes in projective n-space, respectively. For each k between 1 and n-2 there are 2^{d…
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…
Skew Schubert polynomials
Cristian Lenart, Frank Sottile
We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a r…