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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08994 |
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| _version_ | 1866910911419121664 |
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| author | Cornaz, Denis Kerleau, Sébastien Royer, Clément W. |
| author_facet | Cornaz, Denis Kerleau, Sébastien Royer, Clément W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of positive spanning sets with ties to strongly connected digraphs Cornaz, Denis Kerleau, Sébastien Royer, Clément W. Discrete Mathematics Combinatorics Optimization and Control 05C20, 05C50, 15A21, 15B99 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. |
| title | A characterization of positive spanning sets with ties to strongly connected digraphs |
| topic | Discrete Mathematics Combinatorics Optimization and Control 05C20, 05C50, 15A21, 15B99 |
| url | https://arxiv.org/abs/2411.08994 |