{"paper":{"title":"On Multiple Pattern Avoiding Set Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Shattuck, Toufik Mansour, V\\'it Jel\\'inek","submitted_at":"2013-01-28T10:33:24Z","abstract_excerpt":"We study classes of set partitions determined by the avoidance of multiple patterns, applying a natural notion of partition containment that has been introduced by Sagan. We say that two sets S and T of patterns are equivalent if for each n, the number of partitions of size n avoiding all the members of S is the same as the number of those that avoid all the members of T.\n  Our goal is to classify the equivalence classes among two-element pattern sets of several general types. First, we focus on pairs of patterns {\\sigma,\\tau}, where \\sigma\\ is a pattern of size three with at least two distinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6509","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"}