Related papers: Cluster Expansions from Punctured Orbifolds

We prove a generalization of the Expander Mixing Lemma for arbitrary (finite) simplicial complexes. The original lemma states that concentration of the Laplace spectrum of a graph implies combinatorial expansion (which is also referred to…

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…

Cluster-tilted algebras are trivial extensions of tilted algebras. This correspondence induces a surjective map from tilted algebras to cluster-tilted algebras. If B is a cluster-tilted algebra, we use the fibre of B under this map to study…

We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions…

We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these formulas involve a family of polynomials…

We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness…

We prove a general large sieve statement in the context of random walks on subgraphs of a given graph. This can be seen as a generalization of previously known results where one performs a random walk on a group enjoying a strong spectral…

Constellations and hypermaps generalize combinatorial maps, i.e. embedding of graphs in a surface, in terms of factorization of permutations. In this paper, we extend a result of Jackson and Visentin (1990) stating an enumerative relation…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…

In this paper, we study combinatorial properties of quasi-Cartan companions defined by the c-vectors of acyclic skew-symmetrizable cluster algebras. In particular, we show that the diagram of any skew-symmetrizable matrix associated with an…

Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…

We review some recent progress on applications of Cluster Expansions. We focus on a system of classical particles living in a continuous medium and interacting via a stable and tempered pair potential. We review the cluster expansion in…

We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…

Among the mutation finite cluster algebras the tubular ones are a particularly interesting class. We show that all tubular (simply laced) cluster algebras are of exponential growth by two different methods: first by studying the…

A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in…

We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the…

We extend a recently established combinatorial index formula applying to Lie poset algebras of types B, C, and D. Then, using the extended index formula, we determine a characterization of contact Lie poset algebras of types B, C, and D…

The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…

Walks on Young's lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walks that start at $\varnothing$, end at a…

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.