# A corollary of Stanley's Hook Content Formula

## TL;DR

This paper explores the properties of rectangular tableaux derived from partition hook lengths, demonstrating their equal multisets of entries through combinatorial and algebraic methods involving Stanley's Hook Content Formula.

## Contribution

It introduces a novel application of hook lengths to define tableaux and proves their equivalence using both elementary and algebraic techniques.

## Key findings

- The tableaux have identical multisets of entries.
- Elementary combinatorial proof of the tableaux's properties.
- Algebraic proof using Stanley's Hook Content Formula.

## Abstract

We use the hook lengths of a partition to define two rectangular tableaux. We prove these tableaux have equal multisets of entries, first by elementary combinatorial arguments, and then using Stanley's Hook Content Formula and symmetric polynomials.