On uncertainty inequalities related to subcube partitions and additive energy

TL;DR

This paper establishes an uncertainty inequality connecting the additive energy of a Boolean function's support, its degree, and subcube partitions, revealing new insights into their interrelations in combinatorial number theory.

Contribution

It introduces a novel uncertainty inequality linking additive energy, degree, and subcube partitions of Boolean functions, advancing understanding in combinatorial number theory.

Findings

Derived an inequality relating additive energy and subcube partitions.

Showed how the support's additive energy constrains the Boolean function's degree.

Provided theoretical insights into the structure of Boolean functions in combinatorics.

Abstract

The additive energy plays a central role in combinatorial number theory. We show an uncertainty inequality which indicates how the additive energy of support of a Boolean function, its degree and subcube partition are related.