{"paper":{"title":"Patterns in words of ordered set partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dun Qiu, Jeffrey Remmel","submitted_at":"2018-04-19T11:10:27Z","abstract_excerpt":"An ordered set partition of $\\{1,2,\\ldots,n\\}$ is a partition with an ordering on the parts. Let $\\mathcal{OP}_{n,k}$ be the set of ordered set partitions of $[n]$ with $k$ blocks. Godbole, Goyt, Herdan and Pudwell defined $\\mathcal{OP}_{n,k}(\\sigma)$ to be the set of ordered set partitions in $\\mathcal{OP}_{n,k}$ avoiding a permutation pattern $\\sigma$ and obtained the formula for $|\\mathcal{OP}_{n,k}(\\sigma)|$ when the pattern $\\sigma$ is of length $2$. Later, Chen, Dai and Zhou found a formula algebraically for $|\\mathcal{OP}_{n,k}(\\sigma)|$ when the pattern $\\sigma$ is of length $3$.\n  In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07087","kind":"arxiv","version":3},"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"}