A bijective proof of the hook-length formula and its analogs (Q1324681)

The main result of the article is a bijective proof of the multiplicative formula for the dimension of an irreducible representation of the symmetric group, which is usually called the ``hook-length formula.'' We also prove a formula for the Poincaré series for the multiplicity of the isotypic component in the symmetric algebra \(S(V)\) \((V=\mathbb{C}^ n)\) considered as a graded \(S_ n\)-module. We use classical combinatorial interpretations and establish the bijection in their terms.