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 …

Let Q be a quiver without loops and 2-cycles, let A (Q) be the corresponding cluster algebra
and let x be a cluster. We introduce a new class of integer vectors which we call frieze …

This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein
and Retakh. It generalises several earlier results to this situation: A formula for frieze …

We study the connection between Conway-Coxeter frieze patterns and the data of the
minimal resolution of a complex curve singularity: using Popescu-Pampu's notion of the …

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This note generalizes $\mathrm {SL}(k) $-friezes to configurations of numbers in which one
of the boundary rows has been replaced by a ragged edge (described by a juggling …

In this survey chapter, we explain the intricate links between Conway–Coxeter friezes and
cluster combinatorics. More precisely, we provide a formula, relying solely on the shape of …

This work regards the order polytopes arising from the class of generalized snake posets
and their posets of meet-irreducible elements. Among generalized snake posets of the same …

Dynkin functions were introduced by Ringel as a tool to investigate combinatorial properties
of hereditary artin algebras. According to Ringel, a Dynkin function consists of four …

In this article we study mutation of friezes of type D. We provide a combinatorial formula for
the entries in a frieze after mutation. The two main ingredients in the proof include a certain …