论文标题
Charmed Roots和Kroweras补充
Charmed roots and the Kroweras complement
论文作者
论文摘要
尽管对Weyl群体均一列举了非交叉分区和非钉分区，但这两组组合物体之间的确切关系仍然令人沮丧。在本文中，在对称组的情况下，我们给出了一个精确的组合答案：对于任何标准的Coxeter元素，我们在Kreweras补体下的非交叉分区之间构建了一个均等的两次培养，并在理论上是在理论上的Coxeter上，我们称之为自然的循环作用，我们称之为Kroweras Replation。我们的模棱两可的双眼是既具有均等又具有支持性的独特射击，并且根据魅力根的新定义，使用局部规则构建。诱人的根是由Coxeter元素的选择确定的 - 在线性Coxeter元素$（1，2，\ dots，n）$的特殊情况下，我们恢复了非交叉和非固定分区之间的标准射击之一。
Although both noncrossing partitions and nonnesting partitions are uniformly enumerated for Weyl groups, the exact relationship between these two sets of combinatorial objects remains frustratingly mysterious. In this paper, we give a precise combinatorial answer in the case of the symmetric group: for any standard Coxeter element, we construct an equivariant bijection between noncrossing partitions under the Kreweras complement and nonnesting partitions under a Coxeter-theoretically natural cyclic action we call the Kroweras complement. Our equivariant bijection is the unique bijection that is both equivariant and support-preserving, and is built using local rules depending on a new definition of charmed roots. Charmed roots are determined by the choice of Coxeter element -- in the special case of the linear Coxeter element $(1, 2, \dots, n)$, we recover one of the standard bijections between noncrossing and nonnesting partitions.
