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Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs."},"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":"1802.02146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","cross_cats_sorted":[],"title_canon_sha256":"1ee991746617d894d38fe32a6d6c5c26d64a4de50f5b84e763e480e7bfee6678","abstract_canon_sha256":"32dfdfc00932c8abad540afa464ef7be02376d732c8919b32be696ab0d608b59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:09.194712Z","signature_b64":"7o31sbxwP9YZN9r94ebtqTD7or55U4vkJVJ3V0Nfy0IipvB2cT6RxK7RzpoMnUfEOCd3jrimywyb2ANBTy6XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","last_reissued_at":"2026-05-18T00:24:09.194127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:09.194127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the irregularity of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Lele Liu, Liying Kang","submitted_at":"2018-02-06T15:29:51Z","abstract_excerpt":"Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\\in V(H)$. 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Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02146","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.02146","created_at":"2026-05-18T00:24:09.194202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.02146v1","created_at":"2026-05-18T00:24:09.194202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02146","created_at":"2026-05-18T00:24:09.194202+00:00"},{"alias_kind":"pith_short_12","alias_value":"GAC3VMNKP36G","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GAC3VMNKP36GVXSW","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GAC3VMNK","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE","json":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE.json","graph_json":"https://pith.science/api/pith-number/GAC3VMNKP36GVXSWH64FP3KQOE/graph.json","events_json":"https://pith.science/api/pith-number/GAC3VMNKP36GVXSWH64FP3KQOE/events.json","paper":"https://pith.science/paper/GAC3VMNK"},"agent_actions":{"view_html":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE","download_json":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE.json","view_paper":"https://pith.science/paper/GAC3VMNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.02146&json=true","fetch_graph":"https://pith.science/api/pith-number/GAC3VMNKP36GVXSWH64FP3KQOE/graph.json","fetch_events":"https://pith.science/api/pith-number/GAC3VMNKP36GVXSWH64FP3KQOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/action/storage_attestation","attest_author":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/action/author_attestation","sign_citation":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/action/citation_signature","submit_replication":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/action/replication_record"}},"created_at":"2026-05-18T00:24:09.194202+00:00","updated_at":"2026-05-18T00:24:09.194202+00:00"}