Counting Standard Young Tableaux With Restricted Runs
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Publication:6343163
arXiv2006.10205MaRDI QIDQ6343163
Manuel Kauers, Doron Zeilberger
Publication date: 17 June 2020
Abstract: 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.
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