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arXiv 2411.089942024-11cs.DMmath.COmath.OC

正支撑集的刻画及其与强连通有向图的联系

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

Denis Cornaz, Sébastien Kerleau, Clément W. Royer

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AI总结：

本文针对正支撑集完整刻画缺失的问题，通过揭示其与强边连通有向图的推广关系，借鉴有向图耳分解为正支撑集定义了分解结构，推动了正支撑集的刻画研究。

摘要：

正支撑集（PSSs）是通过非负线性组合张成给定线性空间的向量族。尽管某些类别的正支撑集已被充分理解，但正支撑集的完整刻画仍未解决。本文探讨了正支撑集与强边连通有向图之间相对未被研究的关系，前者可视为后者的推广。我们利用这一联系，基于有向图理论中的耳分解，为正支撑集定义了一种分解结构。

英文摘要：

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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