论文标题
圆形排列的订单
An order on circular permutations
论文作者
论文摘要
来自对仿期Weyl群体的研究的动机，在$ s_n $（即$ n $ -cycles）的圆形排列中定义了排名Poset的结构。它与所谓的接收媒介的poset以及affine Symmetric Group $ \ tilde s_n $的间隔是同构的。 POSET是一个半分布的晶格，排名函数（其范围为$ n $）是由涉及反转的某些特殊公式计算的。我们还证明了与Eulerian数字，$ n $ -gon和Young的晶格的一些链接。
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an interval in the affine symmetric group $\tilde S_n$ with the weak order. The poset is a semidistributive lattice, and the rank function, whose range is cubic in $n$, is computed by some special formula involving inversions. We prove also some links with Eulerian numbers, triangulations of an $n$-gon, and Young's lattice.
