Toric braids and (m,n)-parking functions
Toric braids and (m,n)-parking functions
复制标题
环形编织物和 (m,n)-停车功能
作者：
A. Mellit
Carlsson和Mellit在arXiv：1508.06239中的Dyck路径代数构造被解释为复曲面辫子群的“正部分”的表示。然后，某些总和超过$（m，n）$停车功能有关的评价，这种表示对一些特殊的辫子。Bergeron，Garsia，Leven和Xin在arXiv：1404.4616中提出的合成$（km，kn）$-shuffle猜想就是这个关系的一个推论.
The Dyck path algebra construction of Carlsson and Mellit from arXiv:1508.06239 is interpreted as a representation of "the positive part" of the group of toric braids. Then certain sums over $(m,n)$-parking functions are related to evaluations of this representation on some special braids. The compositional $(km,kn)$-shuffle conjecture of Bergeron, Garsia, Leven and Xin from arXiv:1404.4616 is then shown to be a corollary of this relation.