{"paper":{"title":"Edmonds' problem and the membership problem for orbit semigroups of quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"math.RT","authors_text":"Calin Chindris, Daniel Kline","submitted_at":"2020-08-31T14:36:34Z","abstract_excerpt":"A central problem in algebraic complexity, posed by J. Edmonds, asks to decide if the span of a given $l$-tuple $\\V=(\\V_1, \\ldots, \\V_l)$ of $N \\times N$ complex matrices contains a non-singular matrix.\n  In this paper, we provide a quiver invariant theoretic approach to this problem. Viewing $\\V$ as a representation of the $l$-Kronecker quiver $\\K_l$, Edmonds' problem can be rephrased as asking to decide if there exists a semi-invariant on the representation space $(\\CC^{N\\times N})^l$ of weight $(1,-1)$ that does not vanish at $\\V$. In other words, Edmonds' problem is asking to decide if the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.13648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.13648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}