Hardy-Littlewood-Polya's inequality and a new concept of weak majorization

TL;DR

This paper introduces a new concept of weak majorization, generalizes Hardy-Littlewood-Polya's inequality, and explores their applications to trees, providing new insights into majorization theory.

Contribution

A novel weak majorization concept is proposed and Hardy-Littlewood-Polya's inequality is extended to this new framework.

Findings

Introduction of a strong notion of weak majorization

Generalization of Hardy-Littlewood-Polya's inequality

Application of these concepts to tree structures

Abstract

In this paper we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy-Littlewood-Polya's inequality is generalized.