Hook formula and related identities

A new proof of the hook formula for the dimension of representations of the symmetric group is given with the help of identities which are of independent interest. A probabilistic interpretation of the proof and new formulas relating the parameters of the Young diagrams are given.

[1]  Curtis Greene,et al.  Another Probabilistic Method in the Theory of Young Tableaux , 1984, J. Comb. Theory, Ser. A.

[2]  J. S. Frame,et al.  The Hook Graphs of the Symmetric Group , 1954, Canadian Journal of Mathematics.