101 citations · 283 across the 24 of their papers we have counts for
27 papers
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…
Skew-group -categories as Fukaya categories of orbifolds
Claire Amiot, Pierre-Guy Plamondon
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the noti…
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
Xin Fang, Mikhail Gorsky, Yann Palu +2
We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpre…
A generalization of perfectly clustering words and band bricks for certain gentle algebras
Benjamin Dequêne, Mélodie Lapointe, Yann Palu +3
We generalize the perfectly clustering words of Simpson and Puglisi and relate them to band bricks over certain gentle algebras. This allows us to prove a generalization of a conje…
A refined multiplication formula for cluster characters
Bernhard Keller, Pierre-Guy Plamondon, Fan Qin
We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs…
Tame algebras have dense -vector fans
Bernhard Keller, Pierre-Guy Plamondon, Toshiya Yurikusa
The -vector fan of a finite-dimensional algebra is a fan whose rays are the -vectors of its -term presilting objects. We prove that the -vect…
Quivers with potentials and actions of finite abelian groups
Simone Giovannini, Andrea Pasquali, Pierre-Guy Plamondon
Let be a finite abelian group acting on a path algebra by permuting the vertices and preserving the arrowspans. Let be a potential on the quiver which is fixed by…
Associahedra for finite type cluster algebras and minimal relations between -vectors
Arnau Padrol, Yann Palu, Vincent Pilaud +1
We show that the mesh mutations are the minimal relations among the -vectors with respect to any initial seed in any finite type cluster algebra. We then use this a…
A complete derived invariant for gentle algebras via winding numbers and Arf invariants
Claire Amiot, Pierre-Guy Plamondon, Sibylle Schroll
Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In this paper, we further study the properties of admissible dissections and we show that…
-tilting finite gentle algebras are representation-finite
Pierre-Guy Plamondon
We show that a gentle algebra over a field is -tilting finite if and only if it is representation-finite. The proof relies on the "brick--tilting correspondence" of Demonet-I…
Unistructurality of cluster algebras from surfaces without punctures
Véronique Bazier-Matte, Pierre-Guy Plamondon
A cluster algebra is unistructural if the set of its cluster variables determines its clusters and seeds. It is conjectured that all cluster algebras are unistructural. In this pap…
Non-kissing and non-crossing complexes for locally gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, or…
A geometric model for the derived category of gentle algebras
Sebastian Opper, Pierre-Guy Plamondon, Sibylle Schroll
In this paper we construct a geometric model for the triangulated category generated by the simple modules of any graded gentle algebra. This leads to a geometric model of their pe…
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…
Non-kissing complexes and tau-tilting for gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
We interpret the support -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously…
The cluster category of a surface with punctures via group actions
Claire Amiot, Pierre-Guy Plamondon
Given a certain triangulation of a punctured surface with boundary, we construct a new triangulated surface without punctures which covers it. This new surface is naturally equippe…
Cluster characters
Pierre-Guy Plamondon
These are lecture notes from a mini-course given at the CIMPA in Mar del Plata, Argentina, in March 2016. The aim of the course was to introduce cluster characters for 2-Calabi-Yau…
Derived invariants for surface cut algebras II: the punctured case
Claire Amiot, Daniel Labardini-Fragoso, Pierre-Guy Plamondon
For each algebra of global dimension 2 arising from the quiver with potential associated to a triangulation of an unpunctured surface, Amiot-Grimeland have defined an integer-value…
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…
Kac polynomials for canonical algebras
P. -G. Plamondon, O. Schiffmann
We prove that the number of geometrically indecomposable representations of fixed dimension vector d of a canonical algebra C defined over a finite field Fq is given by a polynomia…
Counting friezes in type D_n
Bruce Fontaine, Pierre-Guy Plamondon
We prove that there is an finite number of friezes in type D_n, and we provide a formula to count them. As a corollary, we obtain formulas to count the number of friezes in types B…
Nakajima varieties and repetitive algebras
Bernard Leclerc, Pierre-Guy Plamondon
We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheave…
Linear independence of cluster monomials for skew-symmetric cluster algebras
Giovanni Cerulli Irelli, Bernhard Keller, Daniel Labardini-Fragoso +1
Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choi…
Generic bases for cluster algebras from the cluster category
Pierre-Guy Plamondon
Inspired by recent work of Geiss-Leclerc-Schroer, we use Hom-finite cluster categories to give a good candidate set for a basis of (upper) cluster algebras with coefficients arisin…