{"paper":{"title":"Constraining Strong c-Wilf Equivalence Using Cluster Poset Asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Mitchell Lee","submitted_at":"2018-07-13T05:30:47Z","abstract_excerpt":"Let $\\pi \\in \\mathfrak{S}_m$ and $\\sigma \\in \\mathfrak{S}_n$ be permutations. An occurrence of $\\pi$ in $\\sigma$ as a consecutive pattern is a subsequence $\\sigma_i \\sigma_{i+1} \\cdots \\sigma_{i+m-1}$ of $\\sigma$ with the same order relations as $\\pi$. We say that patterns $\\pi, \\tau \\in \\mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in $\\mathfrak{S}_n$ with exactly $k$ occurrences of $\\pi$ as a consecutive pattern is the same as for $\\tau$. In 2018, Dwyer and Elizalde conjectured (generalizing a conjecture of Elizalde from 2012) that if $\\pi,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04921","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"}