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The weighted hook-length formula II: Complementary formulas

2010/06/09 by Matjaž Konvalinka, Konvalinka, Matjaz
Computer Science · Mathematics · #05A19 #05E10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1006.1865

openalex publication_date 2010/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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