A bijective proof of the hook-length formula for standard immaculate tableaux

TL;DR

This paper provides a direct bijective proof of the hook-length formula specifically for standard immaculate tableaux, connecting combinatorial structures with algebraic formulas in symmetric functions.

Contribution

It introduces a novel bijective proof for the hook-length formula in the context of standard immaculate tableaux, extending combinatorial methods.

Findings

Established a bijective proof for the hook-length formula

Linked standard immaculate tableaux to non-commutative symmetric functions

Extended combinatorial proof techniques to new tableau classes

Abstract

In this paper, we present a direct bijective proof of the hook-length formula for standard immaculate tableaux, which arose in the study of non-commutative symmetric functions. Our proof is along the spirit of Novelli, Pak and Stoyanovskii's combinatorial proof of the hook-length formula for standard Young tableaux.