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Mathematics > Rings and Algebras

arXiv:1409.8177 (math)
[Submitted on 29 Sep 2014 (v1), last revised 26 Jun 2015 (this version, v2)]

Title:A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

Authors:Kyungyong Lee, Li Li, Matthew R. Mills
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Abstract:We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.
Subjects: Rings and Algebras (math.RA); Combinatorics (math.CO)
MSC classes: 13F60
Cite as: arXiv:1409.8177 [math.RA]
  (or arXiv:1409.8177v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.1409.8177
Journal reference: SIGMA 11 (2015), 049, 24 pages
Related DOI: https://doi.org/10.3842/SIGMA.2015.049

Submission history

From: Li Li [view email] [via SIGMA proxy]
[v1] Mon, 29 Sep 2014 16:25:42 UTC (14 KB)
[v2] Fri, 26 Jun 2015 05:23:47 UTC (108 KB)
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