36 citations · 117 across the 18 of their papers we have counts for
19 papers
Cardinalities of Kiselman monoids and their parity asymptotics
Alessandro D'Andrea, Salvatore Stella
The cardinalities of Kiselman's semigroups are known to grow double exponentially in : the sequence converges along the even and odd subsequences…
On the growth of friezes via theta functions
Pierre-Guy Plamondon, Salvatore Stella
We prove that the infinite friezes arising from the tubes of a given cluster algebra of acyclic affine type all have the same growth coefficients. Our proof uses identities satisfi…
The cardinality of Kiselman's semigroups grows double-exponentially
Alessandro D'Andrea, Salvatore Stella
Let denote Ganyushkin-Kudryavtseva-Mazorchuk's generalization of Kiselman's semigroups. We show that the sequence admits finite limits as grows…
Cluster scattering diagrams of acyclic affine type
Nathan Reading, Salvatore Stella
We give an explicit construction of the cluster scattering diagram for any acyclic exchange matrix of affine type. We show that the corresponding cluster scattering fan coincides b…
On the Strength of Chromatic Symmetric Homology for graphs
Alex Chandler, Radmila Sazdanovic, Salvatore Stella +1
In this paper, we investigate the strength of chromatic symmetric homology as a graph invariant. Chromatic symmetric homology is a lift of the chromatic symmetric function for grap…
The action of a Coxeter element on an affine root system
Nathan Reading, Salvatore Stella
The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and their reflection groups. This paper deve…
Affine cluster monomials are generalized minors
Dylan Rupel, Salvatore Stella, Harold Williams
We study the realization of acyclic cluster algebras as coordinate rings of Coxeter double Bruhat cells in Kac-Moody groups. We prove that all cluster monomials with g-vector lying…
Some Consequences of Categorification
Dylan Rupel, Salvatore Stella
Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomi…
A -Tilting Approach to Dissections of Polygons
Vincent Pilaud, Pierre-Guy Plamondon, Salvatore Stella
We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support -tilting simplicial complex of an explicit finite dimensional alge…
An affine almost positive roots model
Nathan Reading, Salvatore Stella
We generalize the almost positive roots model for cluster algebras from finite type to a uniform finite/affine type model. We define the almost positive Schur roots and a com…
Polytopal realizations of finite type -vector fans
Christophe Hohlweg, Vincent Pilaud, Salvatore Stella
This paper shows the polytopality of any finite type -vector fan, acyclic or not. In fact, for any finite Dynkin type , we construct a universal associahedron $\math…
On Generalized Minors and Quiver Representations
Dylan Rupel, Salvatore Stella, Harold Williams
The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, definin…
SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)
Laurent Demonet, Pierre-Guy Plamondon, Dylan Rupel +2
We define a family of generalizations of -tilings to higher dimensions called --tilings. We show that, in each dimension 3 o…
Exchange Relations for Finite Type Cluster Algebras with Acyclic Initial Seed and Principal Coefficients
Salvatore Stella, Pavel Tumarkin
We give an explicit description of all the exchange relations in any finite type cluster algebra with acyclic initial seed and principal coefficients.
The greedy basis equals the theta basis
Man Wai Cheung, Mark Gross, Greg Muller +4
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
Initial-seed recursions and dualities for d-vectors
Nathan Reading, Salvatore Stella
We present an initial-seed-mutation formula for d-vectors of cluster variables in a cluster algebra. We also give two rephrasings of this recursion: one as a duality formula for d-…
Wonder of sine-Gordon Y-systems
Tomoki Nakanishi, Salvatore Stella
The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Tateo in the 90's in the study of the integrable deformation of conformal field theory by the the…
Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type
Tomoki Nakanishi, Salvatore Stella
We provide an explicit Dynkin diagrammatic description of the c-vectors and the d-vectors (the denominator vectors) of any cluster algebra of finite type with principal coefficient…
Polyhedral models for generalized associahedra via Coxeter elements
Salvatore Stella
Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \emph{generalized as…