Surface cluster algebra expansion formulae via loop graphs
Combinatorics
2020-07-01 v2 Representation Theory
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 -symmetric perfect matchings and -compatible pairs of -symmetric perfect matchings, respectively. We simplify and unify these approaches by considering good matchings of loop graphs.
Cite
@article{arxiv.2006.13218,
title = {Surface cluster algebra expansion formulae via loop graphs},
author = {Jon Wilson},
journal= {arXiv preprint arXiv:2006.13218},
year = {2020}
}
Comments
27 pages, 15 figures. Comments welcome. Introduction is extended to justify the assumptions made in Main Theorem. Thanks to Ilke Canakci for spotting the typo in Figure 12