Alek Vainshtein

TL;DR: Cluster algebras, introduced by Fomin and Zelevinsky in 2001, are commutative rings with unit and no zero divisors equipped with a distinguished family of generators (cluster variables) grouped in overlapping subsets of the same cardinality (the rank of the cluster algebra) connected by exchange relations as discussed by the authors.

TL;DR: In this article, Teke et al. presented a survey of the state-of-the-art mathematics departments in Sweden, including the Department of Mathematics, University of Stockholm, S-10691, Stockholm, Sweden (e.g.

TL;DR: In this paper, the authors considered the case of a general matrix of transition exponents and showed that a relevant geometric object in this case is a certain closed 2-form compatible with the cluster algebra structure.

TL;DR: In this paper, an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of points, and conjecture this to be true for an arbitrary number of Ramification points.

TL;DR: This work studies generating functions for the number of permutations on n letters avoiding 132 and an arbitrary permutation ?