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math.QA2003★ 5 cited
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…
math.CO2003
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…