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

Published 11 Sep 2014 in math.CO and math.RT | (1409.3610v2)

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.

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