{"paper":{"title":"Pattern matching in $(213,231)$-avoiding permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Both Emerite Neou, Romeo Rizzi, St\\'ephane Vialette","submitted_at":"2015-11-05T15:08:59Z","abstract_excerpt":"Given permutations $\\sigma \\in S_k$ and $\\pi \\in S_n$ with $k<n$, the \\emph{pattern matching} problem is to decide whether $\\pi$ matches $\\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\\pi$ and $\\sigma$ avoid the two size-$3$ permutations $213$ and $231$. For the special case where only $\\sigma$ avoids $213$ and $231$, we present a $O(max(kn^2,n^2\\log(\\log(n)))$ time algorithm. We extend our research to bivincular patterns that avoid $213$ and $231$ and present a $O(kn^4)$ time algorithm. Finally we look at the related problem of the longest subsequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01770","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":""},"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"}