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An easy construction shows that $f_r(n) \\leq (1+o(1))\\binom{n}{\\lfloor r/2 \\rfloor}$, and we write $c_r$ for the least number such that $f_r(n) \\leq c_r (1+o(1))\\binom{n}{\\lfloor r/2 \\rfloor}$.\n  It was known that $c_r < 1$ for each even $r \\geq 4$, but this was not known for any odd value of $r$. In this short note, we prove that $c_{295}<1$. Our method also shows that $c_r \\rightarrow 0$, an"},"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":"1708.01898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-06T14:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"3dbd07ad9ff989c5a5da951f01d516023e92b0d8cf68ed9e0ed2d73aed74e34f","abstract_canon_sha256":"487b19d21ef10f33e78e2a201edd33a63bc73ba00829bc8b4ceaa7975ba8e9b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:32.825494Z","signature_b64":"STgzd5jhkpMya7c2sY+yddWxH/1ZsebdmHW6MLtotbu3iNSTgy/A75YzRwotRpwbmhYTwvCjHaQYLItGz40zBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15a9cf8515b51aca1e42bcb4c7853b9932c56bf5c3dd3cd91b8f85b2093f36e0","last_reissued_at":"2026-05-18T00:38:32.824836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:32.824836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Bounds for the Graham-Pollak Problem for Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Leader, Ta Sheng Tan","submitted_at":"2017-08-06T14:49:00Z","abstract_excerpt":"For a fixed $r$, let $f_r(n)$ denote the minimum number of complete $r$-partite $r$-graphs needed to partition the complete $r$-graph on $n$ vertices. 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