{"paper":{"title":"On the Lipschitz Constant of the RSK Correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nathan Linial, Nayantara Bhatnagar","submitted_at":"2010-12-08T18:11:30Z","abstract_excerpt":"We view the RSK correspondence as associating to each permutation $\\pi \\in S_n$ a Young diagram $\\lambda=\\lambda(\\pi)$, i.e. a partition of $n$. Suppose now that $\\pi$ is left-multiplied by $t$ transpositions, what is the largest number of cells in $\\lambda$ that can change as a result? It is natural refer to this question as the search for the Lipschitz constant of the RSK correspondence.\n  We show upper bounds on this Lipschitz constant as a function of $t$. For $t=1$, we give a construction of permutations that achieve this bound exactly. For larger $t$ we construct permutations which come "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1819","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"}