Axial distance in a Young tableau ($d_T(i,j)=c_T(i)-c_T(j)$)

The axial distance from label $j$ to label $i$ in a standard Young tableau is the difference of their Young-diagram cell contents. This sign convention makes $c_T(r+1)-c_T(r)$ equal to $+1$ for consecutive entries in a row and $-1$ in a column. The reciprocal distance supplies the diagonal coefficient of Young orthogonal form.