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This paper studies the enumeration problem of the standard Young tableaux in the shifted U-shaped semiclosed model, which is obtained by folding the first cell of the U-shaped in the southwest corner to the northeast corner. Firstly, the SYT-type chart counting problem is transformed into the corresponding nested monomorphic computational problem based on the correspondence between the nested order statistic and the standard Young tableaux. The number of SYT-type charts is obtained by using the solution method of multiple integrals. Then, the counting results are simplified by using the combination identity, combination summation formula and Catalan number. The SYT-type chart counting formula for the model is obtained. Finally, for the case of m = 1, the conclusion of the kind of SYTtype chart in the special case is given.
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Basic Information:
DOI：10.12194/j.ntu.20221127002
China Classification Code:O157.5
Citation Information:
[1]FU Yao,SUN Ping,JIANG Songshui.Enumeration of shifting U-shaped standard Young tableaux[J].Journal of Nantong University (Natural Science Edition),2023,22(02):86-94.DOI:10.12194/j.ntu.20221127002.
2022-11-27
2022
2023-12-01
2023
2
2023-03-14
2023-03-14
2023-03-14