===Dimension of a representation===<br>"Hook lengths"The dimension of the irreducible representation of the symmetric group corresponding to a partition of is equal to the number of different standard Young tableaux that can be obtained from the diagram of the representation.
<br>"Длины крюков"The dimension of the irreducible representation of the symmetric group corresponding to a partition of is equal to the number of different standard Young tableaux that can be obtained from the diagram of the representation.