5 citations · 5 across the 4 of their papers we have counts for
8 papers
Cluster algebras and Weil-Petersson forms
Michael Gekhtman, Michael Shapiro, Alek Vainshtein
In our previous paper we have discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In this paper we co…
Periodic de Bruijn triangles: exact and asymptotic results
B. Shapiro, M. Shapiro, A. Vainshtein
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic for…
A few riddles behind Rolle's theorem
B. Shapiro, M. Shapiro
We call a smooth function of one variable a degree n pseudopolynomial if its n-th derivative has no (real) zeros. An n pseudopolynomial is called hyperbolic if it has exactly n sim…
Cluster algebras and Poisson geometry
M. Gekhtman, M. Shapiro, A. Vainshtein
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union o…
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 .
Stratified spaces formed by totally positive varieties
Sergey Fomin, Michael Shapiro
By a theorem of A.Björner, for every interval in the Bruhat order of a Coxeter group , there exists a stratified space whose strata are labeled by the elements of $[u,v]…