Outputs (2)

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.2018.10.020

We 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.

SL(2)-tilings do not exist in higher dimensions (mostly) (2018)
Journal Article
Demonet, L., Plamondon, P., Rupel, D., Stella, S., & Tumarkin, P. (2018). SL(2)-tilings do not exist in higher dimensions (mostly). Séminaire lotharingien de combinatoire, 76, Article B76d

We define a family of generalizations of SL2-tilings to higher dimensions called ϵ-SL2-tilings. We show that, in each dimension 3 or greater, ϵ-SL2-tilings exist only for certain choices of ϵ. In the case that they exist, we show that they are essent... Read More about SL(2)-tilings do not exist in higher dimensions (mostly).