On linear equations arising in Combinatorics (Part II)

TL;DR

This paper introduces and studies two new classes of vectors related to Farkas' lemma over integers, expanding the theoretical framework in combinatorics and integer linear algebra.

Contribution

It extends the concept of Farkas-related vectors by defining and analyzing two new classes, contributing to the understanding of integer solutions in combinatorial contexts.

Findings

Introduction of two new classes of vectors related to Farkas' lemma

Theoretical properties and relationships of these classes are established

Potential implications for integer linear programming and combinatorics

Abstract

In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.