A characterization of positive spanning sets with ties to strongly connected digraphs
Discrete Mathematics
2025-04-16 v2 Combinatorics
Optimization and Control
Abstract
Positive spanning sets (PSSs) are families of vectors that span a given linear space through non-negative linear combinations. Despite certain classes of PSSs being well understood, a complete characterization of PSSs remains elusive. In this paper, we explore a relatively understudied relationship between positive spanning sets and strongly edge-connected digraphs, in that the former can be viewed as a generalization of the latter. We leverage this connection to define a decomposition structure for positive spanning sets inspired by the ear decomposition from digraph theory.
Cite
@article{arxiv.2411.08994,
title = {A characterization of positive spanning sets with ties to strongly connected digraphs},
author = {Denis Cornaz and Sébastien Kerleau and Clément W. Royer},
journal= {arXiv preprint arXiv:2411.08994},
year = {2025}
}