{"paper":{"title":"Polynomiality of some hook-length statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Greta Panova","submitted_at":"2008-11-21T04:23:17Z","abstract_excerpt":"We prove a conjecture of Okada giving an exact formula for a certain statistic for hook-lengths of partitions:\n\\frac{1}{n!} \\sum_{\\lambda \\vdash n} f_{\\lambda}^2 \\sum_{u \\in \\lambda} \\prod_{i=1}^{r}(h_u^2 - i^2) = \\frac{1}{2(r+1)^2} \\binom{2r}{r}\\binom{2r+2}{r+1} \\prod_{j=0}^{r} (n-j),\nwhere $f_{\\lambda}$ is the number of standard Young tableaux of shape $\\lambda$ and $h_u$ is the hook length of the square $u$ of the Young diagram of $\\lambda$. We also obtain other similar formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3463","kind":"arxiv","version":4},"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"}