Weighted branching formulas for the hook lengths

Ionut Ciocan-Fontanine, Matjaž Konvalinka, Igor Pak

Research output: Contribution to conferencePaperpeer-review

Abstract

The famous hook-length formula is a simple consequence of the branching rule for the hook lengths. While the Greene-Nijenhuis-Wilf probabilistic proof is the most famous proof of the rule, it is not completely combinatorial, and a simple bijection was an open problem for a long time. In this extended abstract, we show an elegant bijective argument that proves a stronger, weighted analogue of the branching rule. Variants of the bijection prove seven other interesting formulas. Another important approach to the formulas is via weighted hook walks; we discuss some results in this area. We present another motivation for our work: J-functions of the Hilbert scheme of points.

Original languageEnglish (US)
Pages259-270
Number of pages12
StatePublished - Dec 1 2010
Event22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States
Duration: Aug 2 2010Aug 6 2010

Other

Other22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
CountryUnited States
CitySan Francisco, CA
Period8/2/108/6/10

Keywords

  • Bijective proofs
  • Hilbert scheme of points
  • Hook-length formula

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