{"paper":{"title":"Normal approximations for descents and inversions of permutations of multisets","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"D. Viswanath, Mark Conger","submitted_at":"2005-08-14T18:55:52Z","abstract_excerpt":"Normal approximations for descents and inversions of permutations of the set $\\{1,2,...,n\\}$ are well known. A number of sequences that occur in practice, such as the human genome and other genomes, contain many repeated elements. Motivated by such examples, we consider the number of inversions of a permutation $\\pi(1), \\pi(2),...,\\pi(n)$ of a multiset with $n$ elements, which is the number of pairs $(i,j)$ with $1\\leq i < j \\leq n$ and $\\pi(i)>\\pi(j)$. The number of descents is the number of $i$ in the range $1\\leq i < n$ such that $\\pi(i) > \\pi(i+1)$. We prove that, appropriately normalized,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508242","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"}