Cluster Expansions from Punctured Orbifolds
Combinatorics
2026-05-07 v1
Abstract
We provide multiple combinatorial expansion formulas - in terms of snake graphs, labelled posets, matrices, and -walks - for elements in generalized cluster algebras associated to arcs on punctured orbifolds and illustrate their equivalence. This work generalizes and unifies existing work on combinatorial expansion formulas from surfaces and unpunctured orbifolds.
Cite
@article{arxiv.2605.04982,
title = {Cluster Expansions from Punctured Orbifolds},
author = {Esther Banaian and Wonwoo Kang and Elizabeth Kelley and Ezgi Kantarcı Oğuz and Emine Yıldırım},
journal= {arXiv preprint arXiv:2605.04982},
year = {2026}
}