Polytopal realizations of non-crystallographic associahedra
(2024)
Journal Article
Felikson, A., Tumarkin, P., & Yildirim, E. (in press). Polytopal realizations of non-crystallographic associahedra. Algebraic combinatorics,
Outputs (27)
Categorifications of non-integer quivers: types H_4, H_3 and I_2(2n + 1) (2024)
Journal Article
Duffield, D. D., & Tumarkin, P. (2024). Categorifications of non-integer quivers: types H_4, H_3 and I_2(2n + 1). Representation Theory, 28(7), https://doi.org/10.1090/ert/671
Cluster algebras of finite mutation type with coefficients (2024)
Journal Article
Felikson, A., & Tumarkin, P. (online). Cluster algebras of finite mutation type with coefficients. Journal of combinatorial algebra, https://doi.org/10.4171/JCA/92We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type. This completes the classification of all mutation-finite cluster algebras started in [FeSTu1].
Categorifications of non-integer quivers: types I_2(2n) (2023)
Preprint / Working Paper
Duffield, D., & Tumarkin, P. Categorifications of non-integer quivers: types I_2(2n)
Mutation-finite quivers with real weights (2023)
Journal Article
Felikson, A., & Tumarkin, P. (2023). Mutation-finite quivers with real weights. Forum of Mathematics, Sigma, 11, Article e9. https://doi.org/10.1017/fms.2023.8We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrisable matrix has a geometric realisation by reflections. We also explore the structure of acyclic represe... Read More about Mutation-finite quivers with real weights.
Friezes for a pair of pants (2022)
Journal Article
Canakci, I., Garcia Elsener, A., Felikson, A., & Tumarkin, P. (2022). Friezes for a pair of pants. Séminaire lotharingien de combinatoire, 86B, Article 32Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the setting of cluster algebras, the notion of a frieze pattern can be genera... Read More about Friezes for a pair of pants.
Cluster algebras from surfaces and extended affine Weyl groups (2021)
Journal Article
Felikson, A., Lawson, J., Shapiro, M., & Tumarkin, P. (2021). Cluster algebras from surfaces and extended affine Weyl groups. Transformation Groups, 26(2), 501-535. https://doi.org/10.1007/s00031-021-09647-yWe characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space V , and with every triangul... Read More about Cluster algebras from surfaces and extended affine Weyl groups.
Geometry of mutation classes of rank 3 quivers (2019)
Journal Article
Felikson, A., & Tumarkin, P. (2019). Geometry of mutation classes of rank 3 quivers. Arnold Mathematical Journal, 5(1), 37-55. https://doi.org/10.1007/s40598-019-00101-2We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by π-rotations for the cyclic ones. The geometr... Read More about Geometry of mutation classes of rank 3 quivers.
Bases for cluster algebras from orbifolds with one marked point (2019)
Journal Article
Canakci, I., & Tumarkin, P. (2019). Bases for cluster algebras from orbifolds with one marked point. Algebraic combinatorics, 2(3), 355-365. https://doi.org/10.5802/alco.48We generalize the construction of the bangle, band and bracelet bases for cluster algebras from unpunctured orbifolds to the case where there is only one marked point on the boundary.
Acyclic cluster algebras, reflection groups, and curves on a punctured disc (2018)
Journal Article
Felikson, A., & Tumarkin, P. (2018). Acyclic cluster algebras, reflection groups, and curves on a punctured disc. Advances in Mathematics, 340, 855-882. https://doi.org/10.1016/j.aim.2018.10.020We establish a bijective correspondence between certain non-self-intersecting curves in an n-punctured disc and positive c-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corollary, we obtai... Read More about Acyclic cluster algebras, reflection groups, and curves on a punctured disc.