On the Tymoczko Codes for Standard Young Tableaux

Given a partition $\lambda$ of integer $n>0$, there exists a diagram (called Young diagram $\mathcal{ Y}_{\lambda}$) associated with $\lambda$. 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 $\lambda$. In this paper, we associate an invariant with each standard Young tableau of shape $\lambda$, and provide some combinatorial interpretations of these invariants.