关于簇代数交换图的性质
组合数学
2016-05-19 v2 辛几何
摘要
我们在两种情形下证明了关于簇代数 的交换图的顶点与边的一个猜想：当 为几何型时，以及当 为任意且其交换矩阵非退化时。在第二种情形我们还证明了交换图不依赖于 的系数。这两个猜想最近由 Fomin 和 Zelevinsky 提出。
引用
@article{arxiv.math/0703151,
title = {On the properties of the exchange graph of a cluster algebra},
author = {Michael Gekhtman and Michael Shapiro and Alek Vainshtein},
journal= {arXiv preprint arXiv:math/0703151},
year = {2016}
}
备注
Former Conjecture 2 split into Conjectures 2 and 3. Former Theorem 3 split into Theorems 4 and 5 accordingly. Former Section 2 split into Sections 2 and 3 accordingly. An error in the proof of case (i) of the former Theorem 3 (now Theorem 4) corrected, see 10 lines after equation (12)