{"paper":{"title":"Feasible combinatorial matrix theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.LO","authors_text":"Ariel Fern\\'andez, Michael Soltys","submitted_at":"2013-03-26T12:30:36Z","abstract_excerpt":"We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, can be proven in the first order theory $\\LA$ with induction restricted to $\\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\\Pi_2^B$ induction, and hence does not yield feasible proofs --- while our new approach does. $\\LA$ is a weak theory that essentially captures the ring properties of matrices; however, equipped with $\\Sigma_1^B$ induction $\\LA$ is capable of proving KMM, and a host of other combinatorial properties such as Men"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6453","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"}