The Hook Graphs of the Symmetric Group

Abstract

Each irreducible representation [λ] of the symmetric group Sn may be identified by a partition [λ] of n into non-negative integral parts λ1 ≥ λ2 ≥ … λn ≥ 0, of which the first λ'j parts are ≥j, or by a right (Young) diagram also called [λ], that contains λi nodes in its ith row and λ'j nodes in its jth column.