{"paper":{"title":"Shape-Wilf-equivalences for vincular patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew M. Baxter","submitted_at":"2012-01-23T16:58:50Z","abstract_excerpt":"We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as \"generalized patterns\" or \"dashed patterns\"). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilf-equivalence. When vincular patterns $\\alpha$ and $\\beta$ are filling-shape-Wilf-equivalent, we prove that the direct sum $\\alpha\\oplus\\sigma$ is filling-shape-Wilf-equivalent to $\\beta\\oplus\\sigma$. We also discover two new pairs of patterns which are filling-shape-Wilf-equivalent: when $\\alpha$, $\\beta$, and $\\sigma$ are nonempty consecutive patterns which are Wilf-equivalent, $\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4767","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"}