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

Emily Gunawan, Gregg Musiker

Research output: Contribution to journalConference articlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)721-732
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2015
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: Jul 6 2015Jul 10 2015

Bibliographical note

Funding Information:
†Email: egunawan@umn.edu. Supported by NSF Grants DMS-1067183 and DMS-1148634. ‡Email: musiker@umn.edu. Supported by NSF Grants DMS-1067183 and DMS-1148634.

Publisher Copyright:
© 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

Keywords

  • Atomic basis
  • Cluster algebra
  • Triangulated surface

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