The greedy basis equals the theta basis: A rank two haiku

Man Wai Cheung; Mark Gross; Greg Muller; Gregg Musiker; Dylan Rupel; Salvatore Stella; Harold Williams

doi:10.1016/j.jcta.2016.08.004

The greedy basis equals the theta basis: A rank two haiku

Man Wai Cheung, Mark Gross, Greg Muller, Gregg Musiker, Dylan Rupel, Salvatore Stella, Harold Williams

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.

Original language	English (US)
Pages (from-to)	150-171
Number of pages	22
Journal	Journal of Combinatorial Theory. Series A
Volume	145
DOIs	https://doi.org/10.1016/j.jcta.2016.08.004
State	Published - Jan 1 2017

Bibliographical note

Publisher Copyright:
© 2016

Keywords

Broken lines
Cluster algebras
Greedy basis
Scattering diagrams
Theta functions

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10.1016/j.jcta.2016.08.004

https://www.repository.cam.ac.uk/handle/1810/260173

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title = "The greedy basis equals the theta basis: A rank two haiku",

abstract = "We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.",

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AU - Musiker, Gregg

AU - Rupel, Dylan

AU - Stella, Salvatore

AU - Williams, Harold

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KW - Scattering diagrams

KW - Theta functions

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The greedy basis equals the theta basis: A rank two haiku

Abstract

Bibliographical note

Keywords

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