A New Class of Linear Relations for Scalar Partitions

TL;DR

This paper introduces a novel algorithm for deriving linear relations in scalar integer partition problems, utilizing Cayley's theorem and variable elimination to simplify the analysis of solutions.

Contribution

It presents a new algorithm that derives linear relations for scalar partitions, advancing the understanding of partition solutions through a reduction method.

Findings

The algorithm effectively derives linear relations for scalar partitions.

It simplifies the analysis of solutions using Cayley's theorem.

The method reduces complex partition problems to manageable forms.

Abstract

A scalar integer partition problem asks for a number of nonnegative integer solutions to a linear Diophantine equation with integer positive coefficients. The manuscript discusses an algorithm of derivation of linear relations involving the finite number of scalar partitions. The algorithm employs the Cayley theorem about the reduction of a double partition to a sum of scalar partitions based on the variable elimination procedure.