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arXiv · 2411.08994

A characterization of positive spanning sets with ties to strongly connected digraphs

Denis Cornaz·Sébastien Kerleau·Clément W. Royer
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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.

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Denis Cornaz, Sébastien Kerleau, Clément W. Royer. 2024-11-13. A characterization of positive spanning sets with ties to strongly connected digraphs. https://arxiv.org/abs/2411.08994

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