2024/11/13 by Cornaz, Denis, Kerleau, Sébastien, Royer, Clément W.
#05C20 #05C50 #15A21 #15B99 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2411.08994
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.