On majorization for polynomials sharing a common interlacer

TL;DR

This paper establishes necessary and sufficient conditions for majorization among real-rooted polynomials sharing an interlacer, introduces the concept of strong majorization, and explores their relationships using residue-based methods.

Contribution

It provides a complete characterization of majorization for polynomials with a common interlacer and introduces the new concept of strong majorization.

Findings

Characterization of majorization via residues and fraction decomposition.

Introduction of strong majorization and its relation to standard majorization.

Framework applicable to real-rooted polynomials sharing an interlacer.

Abstract

We give necessary and sufficient conditions for majorization of realrooted polynomials sharing a common interlacer by means of residues coming from fraction decomposition. We also introduce a motivated notion called strong majorization, and we show how it relates to standard majorization.