Corpus ID: 219792085

Counting Standard Young Tableaux With Restricted Runs

@article{Kauers2020CountingSY,
  title={Counting Standard Young Tableaux With Restricted Runs},
  author={Manuel Kauers and Doron Zeilberger},
  journal={arXiv: Combinatorics},
  year={2020}
}
The number of Young Tableaux whose shape is a k by n rectangle is famously (nk)! 0! ... (k-1)!/((n+k-1)!(n+k-2)!... n!) implying that for each specific k, that sequence satisfies a linear recurrence equation with polynomial coefficients of the first order. But what about counting Young tableaux where certain "run lengths" are forbidden? Then things seem to get much more complicated. We conclude with four conjectures and pledge donations to the OEIS in honor of the first provers. 
1 Citations
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Austria E-mail manuel dot kauers at jku dot at
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