Emily Gunawan ; Gregg Musiker - 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) - https://doi.org/10.46298/dmtcs.2524
Atomic Bases and $T$-path Formula for Cluster Algebras of Type $D$Conference paper

Authors: Emily Gunawan 1; Gregg Musiker 1

  • 1 School of Mathematics

[en]
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 $D$.

[fr]
Nous généralisons une formule de développement en $T$-chemins pour les arcs sur une surface non-perforée aux arcs sur un polygone à une perforation. Nous utilisons cette formule pour donner une preuve combinatoire du fait que les monômes amassées constituent la base atomique d’une algèbre amassée de type $D$.

https://doi.org/10.46298/dmtcs.2524
Source: 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
Imported on: November 21, 2016
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] cluster algebra, triangulated surface, atomic basis
Licence: Attribution 4.0 International (CC BY 4.0)
Funding:
    Source : OpenAIRE Graph
  • Cluster algebras, critical groups, and tropical curves; Funder: National Science Foundation; Code: 1067183
  • RTG in Combinatorics; Funder: National Science Foundation; Code: 1148634

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