{"paper":{"title":"Minimal right determiners of irreducible morphisms in string algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Xiaoxing Wu, Zhaoyong Huang","submitted_at":"2017-03-19T08:56:49Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional string algebra over a field with the quiver $Q$ such that the underlying graph of $Q$ is a tree, and let $|\\Det(\\Lambda)|$ be the number of the minimal right determiners of all irreducible morphisms between indecomposable left $\\Lambda$-modules. Then we have $$|\\Det(\\Lambda)|=2n-p-q-1,$$ where $n$ is the number of vertices in $Q$, $p=|\\{i\\mid i$ is a source in $Q$ with two neighbours$\\}|$ and $q$ is the number of non-zero vertex ideals of $\\Lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06404","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"}