We establish a combinatorial realization of continued fractions as quotients of cardinalities of
sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that …

We study cluster categories arising from marked surfaces (with punctures and non-empty
boundaries). By constructing skewed-gentle algebras, we show that there is a bijection …

The homogeneous coordinate ring of the Grassmannian Gr k, n has a cluster structure
defined in terms of planar diagrams known as Postnikov diagrams. The cluster …

Cluster algebras are combinatorially defined commutative algebras which were introduced
by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized …

We present a new and very concrete connection between cluster algebras and knot theory.
This connection is being made via continued fractions and snake graphs. It is known that the …

In this article, we realize skew-gentle algebras as skew-tiling algebras associated to
admissible partial triangulations of punctured marked surfaces. Based on this, we establish …

Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from
surfaces, each cluster variable is given by a formula whose terms are parametrized by the …

In the context of representation theory of finite dimensional algebras, string algebras have
been extensively studied and most aspects of their representation theory are well …

This paper is a sequel to our previous work in which we found a combinatorial realization of
continued fractions as quotients of the number of perfect matchings of snake graphs. We …

We express cluster variables of type B n and C n in terms of cluster variables of type A n.
Then we associate a cluster tilted bound symmetric quiver Q of type A 2 n− 1 to any seed of …