DOAJ Open Access 2009

Cluster algebras of unpunctured surfaces and snake graphs

Gregg Musiker Ralf Schiffler

Lihat Sumber DOI

Abstrak

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 $G_{T,\gamma}$ .

Topik & Kata Kunci

Mathematics

Penulis (2)

Gregg Musiker

Ralf Schiffler

Format Sitasi

APA MLA BibTeX

Musiker, G., Schiffler, R. (2009). Cluster algebras of unpunctured surfaces and snake graphs. https://doi.org/10.46298/dmtcs.2685

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2685

Informasi Jurnal

Tahun Terbit: 2009
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2685
Akses: Open Access ✓