{"paper":{"title":"Ordered Partitions Avoiding a Permutation of Length 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alvin Y.L. Dai, Robin D.P. Zhou, William Y.C. Chen","submitted_at":"2013-04-11T03:49:20Z","abstract_excerpt":"An ordered partition of $[n]=\\{1, 2, \\ldots, n\\}$ is a partition whose blocks are endowed with a linear order. Let $\\mathcal{OP}_{n,k}$ be set of ordered partitions of $[n]$ with $k$ blocks and $\\mathcal{OP}_{n,k}(\\sigma)$ be set of ordered partitions in $\\mathcal{OP}_{n,k}$ that avoid a pattern $\\sigma$. Recently, Godbole, Goyt, Herdan and Pudwell obtained formulas for the number of ordered partitions of $[n]$ with 3 blocks and the number of ordered partitions of $[n]$ with $n-1$ blocks avoiding a permutation pattern of length 3. They showed that $|\\mathcal{OP}_{n,k}(\\sigma)|=|\\mathcal{OP}_{n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3187","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"}