Cyclic descents for general skew tableaux
Cyclic descents for general skew tableaux
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一般倾斜画面的循环下降
DOI：
10.1016/j.jcta.2019.105120
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Brice Huang
中科院分区：
文献类型：
--
作者：
Brice Huang
标准杨氏表上大小为n的循环下降函数是一个函数，当n被省略时，它限制于通常的下降函数，使得给定形状的标准杨氏表的数量在循环下降集D [n]的任何模n移位下都是不变的。循环下降的概念首先由Rhoades研究矩形，然后由Adin，Elizalde和Roichman推广到某些倾斜形状的家族。Adin、Reiner和Roichman证明了一个斜形状有一个循环下降映射当且仅当它不是一个连通带。不幸的是，他们的证明是非建设性的;到目前为止，显式循环下降映射只知道小家庭的形状。在本文中，我们构造了一个明确的循环下降映射的所有形状，这是可能的。因此，我们对Adin，Reiner和Roichman的结果提供了一个建设性的证明.我们构造的循环下降映射推广了文献中的许多构造。
A cyclic descent function on standard Young tableaux of size n is a function that restricts to the usual descent function when n is omitted, such that the number of standard Young tableaux of given shape with cyclic descent set D⊂[n] is invariant under any modulo n shift of D. The notion of cyclic descent was first studied for rectangles by Rhoades, and then generalized to certain families of skew shapes by Adin, Elizalde, and Roichman. Adin, Reiner, and Roichman proved that a skew shape has a cyclic descent map if and only if it is not a connected ribbon. Unfortunately, their proof is nonconstructive; until now, explicit cyclic descent maps are known only for small families of shapes. In this paper, we construct an explicit cyclic descent map for all shapes where this is possible. We thus provide a constructive proof of Adin, Reiner, and Roichman's result. Our construction of a cyclic descent map generalizes many of the constructions in the literature.