半标准杨表族的提升与循环筛分
Promotion and cyclic sieving on families of SSYT
AI总结：
该研究针对几类半标准杨表，验证其在提升操作下的循环筛分现象，提出计算斜半标准杨表电荷的新方法，推广了此前相关研究结果。
摘要：
我们研究了几类半标准杨表（SSYT），观察到它们在提升（promotion）操作下存在循环筛分现象。第一类是拉伸钩形杨表，我们采用共电荷生成多项式作为CSP（循环筛分现象）多项式。第二类是由矩形构成的斜形杨表，其电荷生成多项式与提升操作共同展现出循环筛分现象，这一结果推广了B. Rhoades以及后续B. Fontaine和J. Kamnitzer的早期研究。最后，我们研究了特定的斜带形杨表，其提升操作的行为具有可预测性，该结果以双循环筛分现象的形式给出。我们使用的工具之一是一种新方法，用于在杨表中每个数字出现频率相同的情况下，计算斜半标准杨表的电荷。
英文摘要：
We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family we consider consists of skew shapes, consisting of rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier result by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in form of a bicyclic sieving phenomenon. One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occur with the same frequency.
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