Hoeffding spaces and Specht modules

TL;DR

This paper establishes a mathematical connection between Hoeffding spaces in permutation-based sampling and irreducible Specht modules of the symmetric group, revealing a deep algebraic structure.

Contribution

It demonstrates that Hoeffding spaces associated with permutations correspond to irreducible Specht modules, linking statistical spaces to algebraic representations.

Findings

Hoeffding spaces carry irreducible symmetric group representations

Each Hoeffding space is equivalent to a two-block Specht module

The result bridges permutation statistics and algebraic representation theory

Abstract

It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.