簇、Coxeter可排序元素与非交叉划分
组合数学
2026-05-13 v2
摘要
我们引入Coxeter群W的Coxeter可排序元素。对有限W，我们给出双射证明：Coxeter可排序元素与簇以及非交叉划分等数。我们用其反集刻画Coxeter可排序元素，并在经典情形中用置换刻画。
引用
@article{arxiv.math/0507186,
title = {Clusters, Coxeter-sortable elements and noncrossing partitions},
author = {Nathan Reading},
journal= {arXiv preprint arXiv:math/0507186},
year = {2026}
}
备注
Minor changes in exposition, including: More precise statement in Remark 6.8; Added Remark 6.9, an observation which is helpful in the sequel (math.CO/0512339); Updated textual references to the sequel and to a paper in preparation (with D. Speyer). 28 pages, 8 figures