Snake Graphs from Triangulated Orbifolds
Combinatorics
2020-12-18 v2
Abstract
We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured orbifolds. In the case of an ordinary arc, this gives a combinatorial proof of positivity to the generalized cluster algebra from this orbifold.
Keywords
Cite
@article{arxiv.2003.13872,
title = {Snake Graphs from Triangulated Orbifolds},
author = {Esther Banaian and Elizabeth Kelley},
journal= {arXiv preprint arXiv:2003.13872},
year = {2020}
}