{"paper":{"title":"Pattern avoidance in ordered set partitions and words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anisse Kasraoui","submitted_at":"2013-07-01T19:53:38Z","abstract_excerpt":"We consider the enumeration of ordered set partitions avoiding a permutation pattern, as introduced by Godbole, Goyt, Herdan and Pudwell. Let $\\op_{n,k}(p)$ be the number of ordered set partitions of $\\{1,2,\\ldots,n\\}$ into $k$ blocks that avoid a permutation pattern $p$. We establish an explicit identity between the number $\\op_{n,k}(p)$ and the numbers of words avoiding the inverse of $p$. This identity allows us to easily translate results on pattern-avoiding words obtained in earlier works into equivalent results on pattern-avoiding ordered set partitions. In particular, \\emph{(a)} we dete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0495","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"}