133 citations · 554 across the 117 of their papers we have counts for
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A sagbi basis for the quantum Grassmannian
Frank Sottile, Bernd Sturmfels
The maximal minors of a p by (m + p) matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated…
Real Rational Curves in Grassmannians
Frank Sottile
Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with…
The special Schubert calculus is real
Frank Sottile
We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for whic…
Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro
Frank Sottile
Boris Shapiro and Michael Shapiro have a conjecture concerning the Schubert calculus and real enumerative geometry and which would give infinitely many families of zero-dimensional…
Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions
Nantel Bergeron, Stefan Mykytiuk, Frank Sottile +1
In his work on P-partitions, Stembridge defined the algebra of peak functions Pi, which is both a subalgebra and a retraction of the algebra of quasi-symmetric functions. We show t…