Skip to Main content Skip to Navigation
Conference papers

Cluster algebras of unpunctured surfaces and snake graphs

Abstract : We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph $G_{T,\gamma}$ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula for these Laurent polynomial expansions in terms of subgraphs of the graph $G_{T,\gamma}$ .
Complete list of metadata

Cited literature [34 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185377
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 11:06:33 AM
Last modification on : Thursday, July 4, 2019 - 11:58:02 AM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:40:37 AM

File

dmAK0156.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185377, version 1

Collections

Citation

Gregg Musiker, Ralf Schiffler. Cluster algebras of unpunctured surfaces and snake graphs. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.673-684. ⟨hal-01185377⟩

Share

Metrics

Record views

82

Files downloads

878