$mathcal{A}_w$中区域的个数小于等于在（强）布吕阿序下比$w$小的排列个数,取等号当且仅当$w$ 避免模式4231, 35142, 42513 和 351624
在本文中,我们证明了$mathcal{A}_w$中区域的个数大于等于在弱布吕阿序下比$w$小的排列个数,取等号当且仅当$w$避免模式231 和 312
） Abstract： For each permutation $w$, we can construct a collection of hyperplanes $mathcal{A}_w$ according to the inversions of $w$, which is called the inversion hyperplane arrangement associated to $w$
It was conjectured by Postnikov and confirmed by Hultman et al
that the number of regions of $mathcal{A}_w$ is less than or equal to the number of permutations below $w$ in the Bruhat order, with the equality holds if and only if $w$ avoids the four patterns 4231, 35142, 42513 and 351624
In this paper, we show that the number of regions of $mathcal{A}_w$ is greater than or equal to the number of permutations below $w$ in the weak Bruhat order, with the equality holds if and only if $w$ avoids the patterns 231 and 312
Keywords： inversion hyperplane arrangement, weak Bruhat order, pattern avoiding 下载PDF阅读器 PDF全文下载： 初稿 （ 0 ） 作者简介： Neil J
Y
Fan, male, assistant professor, major research direction: algebraic combinatorics 通信联系人： 【收录情况】 中国科技论文在线： 范久瑜
逆序超平面排列与弱布吕阿序[EB/OL]
北京：中国科技论文在线
关键词： 逆序超平面排列,弱布吕阿序,模式避免 Neil J
Y
Fan * （ Department of Mathematics, Sichuan University, Chengdu 610064
） 摘要： 对每个排列$w$,我们可以根据$w$的逆序构造一个超平面排列$mathcal{A}_w$,称为$w$对应的逆序超平面排列
这个结果最先是由 Postnikov 提出猜想,后来被Hultman等人证明的
成都 610064
总览 评价 范久瑜 * （ 四川大学数学学院
[2017-02-04]
http://www
paper
edu
cn/releasepaper/content/201702-16
