This article is cited 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

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.

MSC: 13F60; 05E15; 16S99

Received: September 24, 2014; in final form July 9, 2015; Published online July 28, 2015

Language: English

DOI: 10.3842/SIGMA.2015.060

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ArXiv: 1409.3610