On linear equations arising in Combinatorics (Part III)
Masood Aryapoor
TL;DR
This paper explores classes of integer linear equations with Farkas-type properties, extending previous work and showing that systems satisfying Farkas' conditions have special rational solutions.
Contribution
It introduces a new class of integer linear equations with Farkas-type properties and proves the existence of special rational solutions under certain conditions.
Findings
Identified a new class of linear equations with Farkas-type properties
Proved systems satisfying Farkas' lemma have special rational solutions
Extended previous studies on linear equations in combinatorics
Abstract
In the first two papers, the author embarked on a study of classes of linear equations over integers satisfying a "Farkas-type" property. As the third paper in this study, the present paper deals with another class of linear equations over integers that has a similar "Farkas-type" property. Furthermore it is shown that if an arbitrary system of equations over integers satisfies the conditions imposed by Farkas' lemma then it has rational solutions of a special type.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Limits and Structures in Graph Theory