133 citations · 554 across the 117 of their papers we have counts for
6 papers · 1 filter
Rational curves on Grassmannians: systems theory, reality, and transversality
Frank Sottile
We discuss a particular problem of enumerating rational curves on a Grassmannian from several perspectives, including systems theory, real enumerative geometry, and symbolic comput…
Elementary Transversality in the Schubert calculus in any Characteristic
Frank Sottile
We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding interse…
An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2
Frank Sottile
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems…
Complementary Algorithms For Tableaux
Tom Roby, Frank Sottile, Jeffrey Stroomer +1
We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion. The fou…
Some real and unreal enumerative geometry for flag manifolds
Frank Sottile
We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this…
Non-commutative Pieri operators on posets
Nantel Bergeron, Stefan Mykytiuk, Frank Sottile +1
We consider graded representations of the algebra NC of noncommutative symmetric functions on the Z-linear span of a graded poset P. The matrix coefficients of such a representatio…