{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T07:54:33Z","timestamp":1770710073683,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Using existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake graph, due to the authors, is used to derive a formula for the number of signed permutations requiring 4 (burnt) pancake flips to be sorted. We furthermore provide an analogous characterization of the 9-cycles in the burnt pancake graph. Finally we present numerical evidence that polynomial formulae exist giving the number of signed permutations that require $k$ flips to be sorted, with $5\\leq k\\leq9$.<\/jats:p><jats:p>Comment: We have finalized for the paper for publication in DMTCS, updated a   reference to its published version, moved the abstract to its proper   location, and added a thank you to the referees. The paper has 27 pages, 6   figures, and 2 tables<\/jats:p>","DOI":"10.23638\/dmtcs-21-2-5","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:56:18Z","timestamp":1743699378000},"source":"Crossref","is-referenced-by-count":3,"title":["On the number of pancake stacks requiring four flips to be sorted"],"prefix":"10.23638","volume":"Vol. 21 no. 2, Permutation...","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2315-5331","authenticated-orcid":false,"given":"Sa\u00fal A.","family":"Blanco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Buehrle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akshay","family":"Patidar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2019,11,4]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1902.04055v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1902.04055v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:56:19Z","timestamp":1743699379000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/5214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/dmtcs-21-2-5","relation":{"has-preprint":[{"id-type":"arxiv","id":"1902.04055v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1902.04055v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1902.04055","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1902.04055","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,4]]},"article-number":"5214"}}