133 citations · 554 across the 117 of their papers we have counts for
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Experimentation and conjectures in the real Schubert calculus for flag manifolds
James Ruffo, Yuval Sivan, Evgenia Soprunova +1
The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of…
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
Matthias Beck, Christian Haase, Frank Sottile
We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expos…
Real Hessian Curves
Adriana Ortiz-Rodríguez, Frank Sottile
We give some real polynomials in two variables of degrees 4, 5, and 6 whose hessian curves have more connected components than had been known previously. In particular, we give a q…
Line tangents to four triangles in three-dimensional space
Hervé Brönnimann, Olivier Devillers, Sylvain Lazard +1
We investigate the lines tangent to four triangles in R^3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangen…
Tropical Interpolation
Frank Sottile
This short article, which appeared in the MSRI Fall 2004 newletter, is intended for a general mathematical audience. It describes some mathematical themes from the Winter 2004 prog…
Irrational proofs for three theorems of Stanley
Matthias Beck, Frank Sottile
We give new proofs of three theorems of Stanley on generating functions for the integer points in rational cones. The first, Stanley's reciprocity theorem, relates the rational gen…