The CDE property for skew vexillary permutations
The CDE property for skew vexillary permutations
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偏斜轴排列的 CDE 属性
DOI：
10.1016/j.jcta.2019.06.005
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Hopkins, Sam
中科院分区：
文献类型：
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作者：
Hopkins, Sam
我们证明了Reiner，Tenner和Yong的一个猜想，即对应于某些vexillary排列的初始弱序区间具有一致的下度期望（CDE）性质。实际上，我们的定理更一般地适用于某些"斜vexillary"置换（我们引入的概念），并表明这些偏序集实际上是"切换CDE"。作为推论，我们得到了在Barnard和托马斯和威廉姆斯意义下作用于半分配格的行运动的一个同态结果.
We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies more generally to certain “skew vexillary” permutations (a notion we introduce), and shows that these posets are in fact “toggle CDE.” As a corollary we obtain a homomesy result for rowmotion acting on semidistributive lattices in the sense of Barnard and of Thomas and Williams.