论文标题
$ b_n $中完全交换元素的块号，下降和舒尔的积极性
Block number, descents and Schur positivity of fully commutative elements in $B_n$
论文作者
论文摘要
在本文中研究了Coxeter下降的分布和块数量在Hyperoctahedral $ b_n $，$ \ fc（b_n）$中的完全交换元素上的集合。我们证明相关的Chow准合成生成函数等于两个Schur函数的产物的非负值总和。证明涉及将$ \ fc（b_n）$分解为双面barbash-vogan组合细胞的脱节结合，一种$ b $ b $ bubey discent保留的保留涉及$ 321 $的$ \ fc（b_n）$ s_n $ s_n $ s_n $ s_n $ ccos $ s_n $ s_n $ ccos的延伸$ \ fc（b_n）$在称为纤维的不相交子集中。我们还比较了两种不同类型的$ b $ schur积极性概念，这是由chow和poirier的作品引起的
The distribution of Coxeter descents and block number over the set of fully commutative elements in the hyperoctahedral group $B_n$, $\FC(B_n)$, is studied in this paper. We prove that the associated Chow quasi-symmetric generating function is equal to a non-negative sum of products of two Schur functions. The proof involves a decomposition of $\FC(B_n)$ into a disjoint union of two-sided Barbash-Vogan combinatorial cells, a type $B$ extension of Rubey's descent preserving involution on $321$-avoiding permutations and a detailed study of the intersection of $\FC(B_n)$ with $S_n$-cosets which yields a new decomposition of $\FC(B_n)$ into disjoint subsets called fibers. We also compare two different type $B$ Schur-positivity notions, arising from works of Chow and Poirier
