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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 060, 46 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.060 (Mi sigma1041) 		 
This article is cited in 6 scientific papers (total in 6 papers)

$T$-Path Formula and Atomic Bases for Cluster Algebras of Type $D$

Emily Gunawan, Gregg Musiker

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Full-text PDF (896 kB) Citations (6)
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DOI: https://doi.org/10.3842/SIGMA.2015.060
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: cluster algebra; triangulated surface; atomic basis.
Received: September 24, 2014; in final form July 9, 2015; Published online July 28, 2015
Bibliographic databases:
Document Type: Article
MSC: 13F60; 05E15; 16S99
Language: English
Citation: Emily Gunawan, Gregg Musiker, “$T$-Path Formula and Atomic Bases for Cluster Algebras of Type $D$”, SIGMA, 11 (2015), 060, 46 pp.
Citation in format AMSBIB
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\paper $T$-Path Formula and Atomic Bases for Cluster Algebras of Type~$D$
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\vol 11
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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