A cluster expansion formula ($A_n$ case)
| dc.creator | Schiffler, Ralf | |
| dc.date | 2006-11-30 | |
| dc.date | 2007-02-08 | |
| dc.date.accessioned | 2026-07-07T07:45:18Z | |
| dc.date.available | 2026-07-07T07:45:18Z | |
| dc.description | We consider the Ptolemy cluster algebras, which are cluster algebras of finite type $A$ (with non-trivial coefficients) that have been described by Fomin and Zelevinsky using triangulations of a regular polygon. Given any seed $\zS$ in a Ptolemy cluster algebra, we present a formula for the expansion of an arbitrary cluster variable in terms of the cluster variables of the seed $\zS$. Our formula is given in a combinatorial way, using paths on a triangulation of the polygon that corresponds to the seed $\zS$. | |
| dc.description | 9 pages, 2 figures; Version 2: condition (T6) added in Definition 1, Section 2 rewritten, references added | |
| dc.identifier | https://arxiv.org/abs/math/0611956 | |
| dc.identifier | http://arxiv.org/abs/math/0611956 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123487 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S99 (primary); 5E15; 16G20 (secondary) | |
| dc.title | A cluster expansion formula ($A_n$ case) | |
| dc.type | text |