Enumeration of the Standard Young Tableaux of Similar G Shapes

Qiuying Li

《International Core Journal of Engineering》 7卷3期 (2021/03) Pp. 70-76

https://doi.org/10.6919/ICJE.202103_7(3).0011

摘要

This paper considers the enumeration problem of a generalization of standard Young tableaux (SYT) of similar G shapes. The method is to perform multiple integral calculation on the corresponding nested simplex of the complex nesting order statistics that obey the uniform distribution of (0,1). We derive the number of SYT of the truncated hollow shape (k, n^2 )\(n - 2)|{(2,2)} and similar G-shape, it is related to Catalan number. Meanwhile, we obtain the main corollaries, including the cases of (i). k = n, this result is the number of a simple hollow rectangular SYT and (ii). k = n - 1, it is the number of shifted hollow SYT-type chart. Finally, we combine the number of G shape- SYTs with the distribution of the corresponding nested order statistics and apply it to discuss simple voting problems.

關鍵字

Standard Young Tableau ； Nested Order Statistics ； Catalan Number

參考文獻

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