Given a partition λ of integer $n>0$, there exists a diagram (called Young diagram Yλ) associated with λ. The filling of such diagram from $[n]$ such that the entries increase from top to bottom and from left to right is called the standard Young tableaux ($ SYT$) of shape λ. In this paper, we associate an invariant with each standard Young tableau of shape λ, and provide some combinatorial interpretations of these invariants.
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Olasupo et al. (2024) studied this question.
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