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In the case of the top-to-random transposition shuffle we show that there is cutoff at this time with a window of size O(n), provided further that $k\\to\\infty$ as $n\\to\\infty$ (and no cutoff otherwise). For the random-to-random transposition shuffle we show cutoff at time $(1/2)n\\log k$ for the same conditions on $k$. Finally, we analyse the cyclic-to-random transposition shuffle and show partial mixing occurs at time $\\le\\alpha n\\l"},"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":"1302.2601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-11T20:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"f8f3680f7e9dd317b932e0578917c03308356082486e7bb9242dee9fc5b8227f","abstract_canon_sha256":"fc3e62ef7e4b6627c3ddf35fa6e5a2b1fe74da5876741cc19fee57a0a67559b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.648027Z","signature_b64":"uphO3E8/41yzUs/M6s+GJFgTmRkffC+ojPL97YyfLMc/5y/TpxuySO3mbXUd8R5GUjLUlfwhkg7Ner+Qkd1XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c7398764ddbdf996758e825cba21001a2f7f7a0dab7dc765581047ef87225b","last_reissued_at":"2026-05-18T03:34:00.647333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.647333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial mixing of semi-random transposition shuffles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Richard Pymar","submitted_at":"2013-02-11T20:27:45Z","abstract_excerpt":"We show that for any semi-random transposition shuffle on $n$ cards, the mixing time of any given $k$ cards is at most $n\\log k$, provided $k=o((n/\\log n)^{1/2})$. 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