{"paper":{"title":"Outside nested decompositions of skew diagrams and Schur function determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emma Yu Jin","submitted_at":"2016-06-06T14:38:57Z","abstract_excerpt":"In this paper we describe the thickened strips and the outside nested decompositions of any skew shape $\\lambda/\\mu$. For any such decomposition $\\Phi=(\\Theta_1,\\Theta_2,\\ldots,\\Theta_g)$ of the skew shape $\\lambda/\\mu$ where $\\Theta_i$ is a thickened strip for every $i$, if $r$ is the number of boxes that are contained in any two distinct thickened strips of $\\Phi$, we establish a determinantal formula of the function $s_{\\lambda/\\mu}(X)p_{1^r}(X)$ with the Schur functions of thickened strips as entries, where $s_{\\lambda/\\mu}(X)$ is the Schur function of the skew shape $\\lambda/\\mu$ and $p_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01764","kind":"arxiv","version":2},"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"}