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 $D$.

Source : oai:HAL:hal-01337779v1

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

Section: Proceedings

Published on: January 1, 2015

Submitted on: November 21, 2016

Keywords: cluster algebra,triangulated surface,atomic basis,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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