{"paper":{"title":"Frame patterns in n-cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeffrey Remmel, Miles Jones, Sergey Kitaev","submitted_at":"2013-11-13T22:56:41Z","abstract_excerpt":"In this paper, we study the distribution of the number of occurrences of the simplest frame pattern, called the $\\mu$ pattern, in $n$-cycles. Given an $n$-cycle $C$, we say that a pair $\\langle i,j \\rangle$ matches the $\\mu$ pattern if $i < j$ and as we traverse around $C$ in a clockwise direction starting at $i$ and ending at $j$, we never encounter a $k$ with $i < k < j$. We say that $ \\langle i,j \\rangle$ is a nontrivial $\\mu$-match if $i+1 < j$. Also, an $n$-cycle $C$ is incontractible if there is no $i$ such that $i+1$ immediately follows $i$ in $C$.\n  We show that the number of incontrac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3332","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"}