Surface cluster algebra expansion formulae via loop graphs
classification
🧮 math.CO
math.RT
keywords
formulaegammamatchingsclusterexpansiongraphsloopperfect
read the original abstract
In 2011 Musiker, Schiffler and Williams obtained expansion formulae for cluster algebras from orientable surfaces. For singly and doubly notched arcs these formulae required the notion of $\gamma$-symmetric perfect matchings and $\gamma$-compatible pairs of $\gamma$-symmetric perfect matchings, respectively. We simplify and unify these approaches by considering good matchings of loop graphs.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Unimodality and Cluster Algebras from Surfaces
Proves unimodality of rank polynomials for loop fence posets and tagged arcs arising from cluster algebras on surfaces, plus almost interlacing symmetry and a log-concavity conjecture for single-curve laminations.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.