Generalized snake graphs from orbifolds

Elizabeth Kelley
Friday, February 28, 2020 - 3:35pm to 4:25pm
Vincent Hall 570

Cluster algebras, as originally defined by Fomin and Zelevinsky, are characterized by binomial exchange relations. A natural generalization of cluster algebras, due to Chekhov and Shapiro, allows the exchange relations to have arbitrarily many terms. A subset of these generalized cluster algebras can be associated with triangulations of orbifolds, analogous to the subset of ordinary cluster algebras associated with triangulated surfaces. We generalize Musiker-Schiffler-Williams’ snake graph construction for this subset of generalized cluster algebras, yielding explicit combinatorial formulas for the cluster variables. We then show that our construction can be extended to give expansions for generalized arcs on triangulated orbifolds. This is joint work with Esther Banaian.