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.

翻译：正生成集（PSSs）是指能够通过非负线性组合生成给定线性空间的向量族。尽管某些类别的正生成集已得到充分研究，但对其完整的特征刻画仍不明确。本文探讨了正生成集与强边连通有向图之间一个相对未被充分研究的关系：前者可视为后者的推广。我们利用这一关联，借鉴有向图理论中的耳分解思想，为正生成集定义了一种分解结构。