Majorization and R\'enyi Entropy Inequalities via Sperner Theory

TL;DR

This paper explores the connection between majorization, Sperner theory, and R\'enyi entropy inequalities, leading to new bounds for sums of independent, integer-valued random variables.

Contribution

It introduces a novel link between majorization and Sperner posets, deriving new R\'enyi entropy inequalities for sums of independent, integer-valued variables.

Findings

New R\'enyi entropy inequalities established

Connection between majorization and Sperner theory demonstrated

Implications for sums of independent, integer-valued random variables

Abstract

A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random variables.