5 citations · 7 across the 4 of their papers we have counts for
5 papers · 1 filter
Counting real rational functions with all real critical values
B. Shapiro, A. Vainshtein
We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real crit…
The number of connected components in the double Bruhat cells for nonsimply-laced groups
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
We compute the number of connected components in a generic real double Bruhat cell for series and and an exceptional group .
Simply-laced Coxeter groups and groups generated by symplectic transvections
Boris Shapiro, Michael Shapiro, Alek Vainshtein +1
Let W be an arbitrary Coxeter group of simply-laced type (possibly infinite but of finite rank), u,v be any two elements in W, and i be a reduced word (of length m) for the pair (u…
The number of ramified coverings of the sphere by the torus and surfaces of higher genera
P. P. Goulden, D. M. Jackson, A. Vainshtein
We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conject…
Skew-symmetric Vanishing Lattices and Intersections of Schubert Cells
B. Shapiro, M. Shapiro, A. Vainshtein
We prove that the number of connected components in the intersection of two open opposite Schubert cells in the variety of complete real n-dimensional flags equals 3*2^{n-1} for n>…