A Majorization Order on Monomials and Termination of a Successive Difference Substitution Algorithm

TL;DR

This paper introduces a majorization order on monomials to analyze the termination behavior of a successive difference substitution algorithm for polynomial forms.

Contribution

It proposes a new majorization order on monomials and uses it to establish a necessary condition for the positive termination of the KSDS algorithm.

Findings

Established a majorization order on monomials.

Derived a necessary condition for algorithm termination.

Provided insights into polynomial form analysis.

Abstract

We introduce a majorization order on monomials. With the help of this order, we derive a necessary condition on the positive termination of a general successive difference substitution algorithm (KSDS) for an input form $f$.