The weighted hook length formula III: Shifted tableaux

TL;DR

This paper extends the hook length formula to shifted tableaux, providing a bijective proof, variants including weighted versions, and initial steps toward similar proofs for d-complete posets.

Contribution

It introduces a bijective proof of the hook length formula for shifted tableaux and explores weighted variants and preliminary work on d-complete posets.

Findings

Bijective proof of the hook length formula for shifted tableaux

Variants of the branching rule including weighted versions

Initial steps toward bijective proofs for d-complete posets

Abstract

Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux; present variants of this rule, including weighted versions; and make the first tentative steps toward a bijective proof of the hook length formula for d-complete posets.