T -path formula and atomic bases for cluster algebras of type D

Emily Gunawan; Gregg Musiker

doi:10.3842/SIGMA.2015.060

T -path formula and atomic bases for cluster algebras of type D

Emily Gunawan, Gregg Musiker

Mathematics

Research output: Contribution to journal › Article

5 Scopus citations

Abstract

We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.

Original language	English (US)
Article number	060
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	11
DOIs	https://doi.org/10.3842/SIGMA.2015.060
State	Published - Aug 12 2015

Keywords

Atomic basis
Cluster algebra
Triangulated surface

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10.3842/SIGMA.2015.060

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Gunawan, E., & Musiker, G. (2015). T -path formula and atomic bases for cluster algebras of type D. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 11, [060]. https://doi.org/10.3842/SIGMA.2015.060

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abstract = "We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.",

keywords = "Atomic basis, Cluster algebra, Triangulated surface",

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AU - Musiker, Gregg

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KW - Triangulated surface

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