Thus:formula_2Similarly, the dimension of the irreducible representation of corresponding to the partition "λ" of "n" (with at most "r" parts) is the number of semistandard Young tableaux of shape "λ" (containing only the entries from 1 to "r"), which is given by the hook-length formula::formula_3where the index "i" gives the row and "j" the column of a box.
Thus:formula_2Similarly, the dimension of the irreducible representation of corresponding to the partition "λ" of "n" (with at most "r" parts) is the number of semistandard Young tableaux of shape "λ" (containing only the entries from 1 to "r"), which is given by the hook-length formula::formula_3where the index "i" gives the row and "j" the column of a box.