{"paper":{"title":"Unimodality of partitions with distinct parts inside Ferrers shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Fabrizio Zanello, Richard P. Stanley","submitted_at":"2013-05-27T00:44:13Z","abstract_excerpt":"We investigate the rank-generating function $F_{\\lambda}$ of the poset of partitions contained inside a given shifted Ferrers shape $\\lambda$. When $\\lambda $ has four parts, we show that $F_{\\lambda}$ is unimodal when $\\lambda =\\langle n,n-1,n-2,n-3 \\rangle$, for any $n\\ge 4$, and that unimodality fails for the doubly-indexed, infinite family of partitions of the form $\\lambda=\\langle n,n-t,n-2t,n-3t \\rangle$, for any given $t\\ge 2$ and $n$ large enough with respect to $t$.\n  When $\\lambda $ has $b\\le 3$ parts, we show that our rank-generating functions $F_{\\lambda}$ are all unimodal. However"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6083","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"}