论文标题
环的非交叉分区
Noncrossing partitions of an annulus
论文作者
论文摘要
与Coxeter组$ W $和Coxeter Element $ c $相关的非交叉分区POSET是Interval $ [1，C] _T $在$ W $上的绝对顺序中。我们使用Planar图（仿射类型$ \ tilde a $和$ \ tilde c $ offine of本文中的$ w $ of Clance offine类型的$ W $构建新模型，并在本文中使用$ \ tyde $ \ tilde d $和$ \ tilde b $在续集中）。类型$ \ tilde a $中的模型由环的非交叉分区组成。在类型的$ \ tilde c $中，该模型由具有两个orbifold点的磁盘的环或非交叉分区的对称非交叉分区组成。按照麦卡蒙德和苏威尔的领先优势，我们通过将翻译（以$ [1，c] _t $的形式考虑到晶格$ [1，c] _t $，但是平面图的组合学使我们能够在如何进行因素方面做出不同的选择。
The noncrossing partition poset associated to a Coxeter group $W$ and Coxeter element $c$ is the interval $[1,c]_T$ in the absolute order on $W$. We construct a new model of noncrossing partititions for $W$ of classical affine type, using planar diagrams (affine types $\tilde A$ and $\tilde C$ in this paper and affine types $\tilde D$ and $\tilde B$ in the sequel). The model in type $\tilde A$ consists of noncrossing partitions of an annulus. In type $\tilde C$, the model consists of symmetric noncrossing partitions of an annulus or noncrossing partitions of a disk with two orbifold points. Following the lead of McCammond and Sulway, we complete $[1,c]_T$ to a lattice by factoring the translations in $[1,c]_T$, but the combinatorics of the planar diagrams leads us to make different choices about how to factor.
