## Gunawan, Emily and Musiker, Gregg - Atomic Bases and $T$-path Formula for Cluster Algebras of Type $D$

dmtcs:2524 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Atomic Bases and $T$-path Formula for Cluster Algebras of Type $D$

Authors: Gunawan, Emily and Musiker, Gregg

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]