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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2020 Volume 16, 138, 50 pp. (Mi sigma1674)

This article is cited in 1 paper

Snake Graphs from Triangulated Orbifolds

Esther Banaian, Elizabeth Kelley

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

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: generalized cluster algebra, cluster algebra, orbifold, snake graph.

MSC: 05E15, 05C70, 16S99

Received: March 31, 2020; in final form December 8, 2020; Published online December 17, 2020

Language: English

DOI: 10.3842/SIGMA.2020.138



Bibliographic databases:
ArXiv: 2003.13872


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