The weighted hook-length formula II: Complementary formulas

Mathematics – Combinatorics

Scientific paper

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20 pages, 9 figures

Scientific paper

Recently, a new weighted generalization of the branching rule for the hook
lengths, equivalent to the hook formula, was proved. In this paper, we
generalize the complementary branching rule, which can be used to prove
Burnside's formula. We present three different proofs: bijective, via weighted
hook walks, and via the ordinary weighted branching rule.

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