{"paper":{"title":"Robinson-Schensted shapes arising from cycle decompositions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Feigert, Jonathan Meddaugh, Kyle Rosengartner, Mark R. Sepanski, Markus Hunziker, Martha Du Preez, Mitchell Minyard, William Q. Erickson","submitted_at":"2024-12-24T00:08:02Z","abstract_excerpt":"In the symmetric group $S_n$, each element $\\sigma$ has an associated cycle type $\\alpha$, a partition of $n$ that identifies the conjugacy class of $\\sigma$. The Robinson-Schensted (RS) correspondence links each $\\sigma$ to another partition $\\lambda$ of $n$, representing the shape of the pair of Young tableaux produced by applying the RS row-insertion algorithm to $\\sigma$. Surprisingly, the relationship between these two partitions, namely the cycle type $\\alpha$ and the RS shape $\\lambda$, has only recently become a subject of study. In this work, we explicitly describe the set of RS shape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18058","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.18058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}