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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,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0508242","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2005-08-14T18:55:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4c644afe4259478ae4b19cba3906efc1f4851aa07fd812248e92a0aa8db98531","abstract_canon_sha256":"4c8b8ba838eb49859e52be338b960d4c32ceeaa2dedb36a32a98dff24ed61c60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.379590Z","signature_b64":"Kx5n92ByCTUkFghHvmhcUVtsjA4vKd1e/mXATMlhXEool4kdiPRRDAmATy6NJ+J0X7+4jgCNpN1JMYSl4REpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f026a7e967d0e1969ab17ce0bb986ae22f1463baaf2fb9789c68a2e65ff9d13d","last_reissued_at":"2026-05-18T02:44:07.379006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.379006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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