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We present an algorithm with the average number of flips, needed to sort a stack of n burnt pancakes, equal to 7n/4+O(1) and a randomized algorithm for the unburnt version with at most 17n/12+O(1) flips on average.\n  In addition, we show that in the burnt version, the average number of flips of any a"},"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":"0901.3119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2009-01-20T20:08:57Z","cross_cats_sorted":[],"title_canon_sha256":"0fbdfbaf70930def469e7a21f0bdd6346e0a4ad2e6741b5a4520ad85a531fefa","abstract_canon_sha256":"527abb4dd9b60284ace3237f63e5269948c7c913b36b08ff5971cff98a2d4054"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.948412Z","signature_b64":"lU4X/rNoyPqW/abEg7wHmGRxUe8LPplMvEbUTyneUuT1jtaf1pX94UVGd4p8JAopomTQuASRu6JxBhX22VTCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4fc22966745f163a4037140ac4bbb50712ea56b3dc64712442e874511fffe55","last_reissued_at":"2026-05-18T04:30:03.947982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.947982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average number of flips in pancake sorting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Josef Cibulka","submitted_at":"2009-01-20T20:08:57Z","abstract_excerpt":"We are given a stack of pancakes of different sizes and the only allowed operation is to take several pancakes from top and flip them. 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