{"paper":{"title":"On the Vector Linear Solvability of Networks and Discrete Polymatroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. Sundar Rajan, Vijayvaradharaj T. Muralidharan","submitted_at":"2013-01-14T15:03:12Z","abstract_excerpt":"We consider the vector linear solvability of networks over a field $\\mathbb{F}_q.$ It is well known that a scalar linear solution over $\\mathbb{F}_q$ exists for a network if and only if the network is \\textit{matroidal} with respect to a \\textit{matroid} representable over $\\mathbb{F}_q.$ A \\textit{discrete polymatroid} is the multi-set analogue of a matroid. In this paper, a \\textit{discrete polymatroidal} network is defined and it is shown that a vector linear solution over a field $\\mathbb{F}_q$ exists for a network if and only if the network is discrete polymatroidal with respect to a disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3003","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}