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Sapientiae, Informatica 6 (2014) 132-158), we show that $$\\alpha(H)\\geq \\sum_{u\\in V(H)}f_r(d_H(u))$$ for an $r$-uniform linear triangle-free hypergraph $H$ with $r\\geq 2$, where \\"},"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":"1507.04323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-15T18:51:06Z","cross_cats_sorted":[],"title_canon_sha256":"58ada3180c6a44b53e0cd7973108b7c44e9c9b5ddf2adbafbd8e42981fb602c0","abstract_canon_sha256":"3658398f4986865bd2dc6fec0044b9f71e60ddfa90c0d714bc768c0b2142604a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:48.659696Z","signature_b64":"1Zc/6G6RSPIqbEbYOhpUmGnTorIMGGpFu77a7ALAVSPoH5l/fIK2H6CSAgNBYJDkQK98cFBUJIb5Yw+wVWm5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9872e4a6fe964ce8a8955a2b828a258191cee8e963d49a17a16c25b7457aae5","last_reissued_at":"2026-05-18T01:36:48.659258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:48.659258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Independence in Uniform Linear Triangle-free Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian L\\\"owenstein, Dieter Rautenbach, Michael Gentner, Piotr Borowiecki","submitted_at":"2015-07-15T18:51:06Z","abstract_excerpt":"The independence number $\\alpha(H)$ of a hypergraph $H$ is the maximum cardinality of a set of vertices of $H$ that does not contain an edge of $H$. 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