Abstract

We study the Young lattice with the edge multiplicitiesϰ α (λ, ⋏) arising in the simplest Pieri formula for Jack symmetric polynomialsP λ (x; α) with parameter α. A new proof of Stanley’s α-version of the hook formula is given. We also prove the formula whereϕ(λ) = ∏ b∈λ (a(b)α +l(b) + 1)−1 andc α(b) is the α-contents of the new boxb=⋏/λ.

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