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Promotion and cyclic sieving on families of SSYT

Per Alexandersson Department of Mathematics, Stockholm University, Stockholm, Sweden Ezgi Kantarci Oğuz Department of Mathematics, KTH-Royal Institute of Technology, Stockholm, Sweden Svante Linusson Department of Mathematics, KTH-Royal Institute of Technology, Stockholm, Sweden

TBD mathscidoc:2203.43020

Arkiv for Matematik, 59, (2), 247-274, 2021.11
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 contains skew shapes, consisting of disjoint rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier results 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 the 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 occurs with the same frequency.
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@inproceedings{per2021promotion,
  title={Promotion and cyclic sieving on families of SSYT},
  author={Per Alexandersson, Ezgi Kantarci Oğuz, and Svante Linusson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311110305104543960},
  booktitle={Arkiv for Matematik},
  volume={59},
  number={2},
  pages={247-274},
  year={2021},
}
Per Alexandersson, Ezgi Kantarci Oğuz, and Svante Linusson. Promotion and cyclic sieving on families of SSYT. 2021. Vol. 59. In Arkiv for Matematik. pp.247-274. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311110305104543960.
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