5 citations · 7 across the 4 of their papers we have counts for
14 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…
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…
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 .
Counting occurences of 132 in a permutation
Toufik Mansour, Alek Vainshtein
We study the generating function for the number of permutations on n letters containing exactly $r\gs0$ occurences of 132. It is shown that finding this function for a given r amou…