相关论文: On Leclerc's conjectural cluster structures for op…

A cluster is a finite set of generators of a cluster algebra. The Laurent Phenomenon of Fomin and Zelevinsky says that any element of a cluster algebra can be written as a Laurent polynomial in terms of any cluster. The upper cluster…

In this paper, I construct Chern classes in the rigid cohomology of P. Berthelot. We start by constructing Chern classes for proper varieties. To prove all the properties we have to reinterpret the construction in a crystalline way. Then we…

We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.

This work aims at improving the quality of structural variant prediction from the mapped reads of a sequenced genome. We suggest a new model based on cluster editing in weighted graphs and introduce a new heuristic algorithm that allows to…

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in a previous paper of the authors. The present paper studies bundles which compute these Clifford indices. We show that under…

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new…

This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.

Let $X$ be a smooth projective scheme and $E$ a vector bundle on $X$. For a relative hypersurface $Y_f \subset \mathbb{P}(E)$ of degree $d$ defined by a global section $f$, we establish a functorial equivalence between the category of…

We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described…

We study cluster algebras that are associated to unpunctured surfaces with coefficients arising from boundary arcs. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of…

In this paper, we review or introduce several differential structures on manifolds in the general setting of real and complex differential geometry, and apply this study to Teichm\"uller theory. We focus on bi-Lagrangian i.e. para-K\"ahler…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…

In a survey paper in 2011, Amiot proposed a conjectural characterisation of the cluster categories which were conceived in the mid 2000s to lift the combinatorics of Fomin-Zelevinsky's cluster algebras to the categorical level. This paper…

We study the geometry of the varieties of clusters X_r introduced by Kleiman in the 70's, showing that for every Enriques diagram D of r vertices the subset Cl(D) of the clusters with Enriques diagram D is locally closed. We study also the…

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize the standard Clifford relation between (pseudo)-Riemannian metric structures and Dirac matrices. We show for flat…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

Associated to any acyclic cluster algebra is a corresponding triangulated category known as the cluster category. It is known that there is a one-to-one correspondence between cluster variables in the cluster algebra and exceptional…

In this paper, we show that the subcategory $\mathscr{C}_{w,v}$ of modules over quiver Hecke algebras is a monoidal categorification of the coordinate ring of any open Richardson variety of Dynkin types after inverting the frozen cluster…

Due to its rich structure and close connection with gauge theory, hyperk\"ahler manifolds have attracted increasing interest. Using infinite dimensional hyperk\"ahler reduction, Kronheimer proved that certain adjoint orbits of complexified…