论文标题
促进和循环筛分Ssyt家族
Promotion and cyclic sieving on families of SSYT
论文作者
论文摘要
我们检查了一些Semistandard Young Tableaux的家庭，为此我们观察到了促进的循环筛分现象。 我们认为的第一个家庭由拉伸的挂钩形状组成，我们将产生多项式的Coharge用作CSP多项式。 我们认为的第二个家庭由偏斜的形状组成，由矩形组成。同样，产生多项式和促进的电荷表现出环状筛分现象。这是Rhoades和后来的B. Fontaine和J. Kamnitzer的早期结果。 最后，我们考虑了某些偏斜的丝带，其中促销以可预测的方式行为。该结果以双环筛分现象的形式说明。 我们使用的工具之一是一种新的方法来计算偏斜的偏度tableaux的电荷，而在Tableau中的每个数字都以相同的频率出现时。
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.
