The Hook Graphs of the Symmetric Group

Source abstract

Each irreducible representation [λ] of the symmetric group S n may be identified by a partition [λ] of n into non-negative integral parts λ 1 ≥ λ 2 ≥ … λ n ≥ 0, of which the first λ' j parts are ≥ j , or by a right (Young) diagram also called [λ], that contains λ i nodes in its ith row and λ' j nodes in its jth column.