{"paper":{"title":"Vincular pattern posets and the M\\\"obius function of the quasi-consecutive pattern poset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antonio Bernini, Luca Ferrari","submitted_at":"2014-10-22T14:11:51Z","abstract_excerpt":"We introduce vincular pattern posets, then we consider in particular the quasi-consecutive pattern poset, which is defined by declaring $\\sigma \\leq \\tau$ whenever the permutation $\\tau$ contains an occurrence of the permutation $\\sigma$ in which all the entries are adjacent in $\\tau$ except at most the first and the second. We investigate the M\\\"obius function of the quasi-consecutive pattern poset and we completely determine it for those intervals $[\\sigma ,\\tau ]$ such that $\\sigma$ occurs precisely once in $\\tau$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6046","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"}