A cluster expansion formula ($A_n$ case)
表示论
2007-05-23 v2 环与代数
摘要
We consider the Ptolemy cluster algebras, which are cluster algebras of finite type (with non-trivial coefficients) that have been described by Fomin and Zelevinsky using triangulations of a regular polygon. Given any seed 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 . Our formula is given in a combinatorial way, using paths on a triangulation of the polygon that corresponds to the seed .
引用
@article{arxiv.math/0611956,
title = {A cluster expansion formula ($A_n$ case)},
author = {Ralf Schiffler},
journal= {arXiv preprint arXiv:math/0611956},
year = {2007}
}
备注
9 pages, 2 figures; Version 2: condition (T6) added in Definition 1, Section 2 rewritten, references added