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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 $\\Lambda$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.06404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-19T08:56:49Z","cross_cats_sorted":[],"title_canon_sha256":"13c43d152482b2a20755a270d93e6543b5ef300fb166092da93f1645f877970a","abstract_canon_sha256":"4530395cf77956c567eb73a8cb6e82cb222f1d6922e6acde11ae93145bdd1da6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:23.003288Z","signature_b64":"xUFSnJt8XiLqHRz5YkcGUTca6B4fuexn365ixsRCITDgsJYGh1W5zPkuOZdMJbzuokF3eVYZbDxlG4tCkho7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c074d29c23d4d14163c05bb3face23e7ad58a55cc388dab20b2f0cf1f80caedd","last_reissued_at":"2026-05-18T00:48:23.002677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:23.002677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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