{"paper":{"title":"Symmetric functions and the principal case of the Frankl-F\\\"uredi conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. Nikiforov","submitted_at":"2018-02-27T18:56:55Z","abstract_excerpt":"Let $r\\geq3$ and $G$ be an $r$-uniform hypergraph with vertex set $\\left\\{ 1,\\ldots,n\\right\\} $ and edge set $E$. Let \\[ \\mu\\left( G\\right) :=\\max {\\textstyle\\sum\\limits_{\\left\\{ i_{1},\\ldots,i_{r}\\right\\} \\in E}} x_{i_{1}}\\cdots x_{i_{r}}, \\] where the maximum is taken over all nonnegative $x_{1},\\ldots,x_{n}$ with $x_{1}+\\cdots+x_{n}=1.$\n  Let $t\\geq r-1$ be the unique real number such that $\\left\\vert E\\right\\vert =\\binom{t}{r}$. It is shown that if $r\\leq5$ or $t\\geq4\\left( r-1\\right) \\left( r-2\\right) $, then \\[ \\mu\\left( G\\right) \\leq t^{-r}\\binom{t}{r}% \\] with equality holding if and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10075","kind":"arxiv","version":3},"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"}