An alternative proof of an identity related to Type IV superorthogonality

Yixuan Pang

Published 2023-12-24Version 1

We provide an alternative proof of an algebraic identity, which can be used to prove the direct and the converse inequality under Type IV superorthogonality. Our arguments are more symmetric and connect superorthogonality with enumerative combinatorics. As an application, we significantly improve upon a previous bound for the formal constant in the direct inequality. We also introduce variants of Type IV superorthogonality, under which we prove the converse inequality.