{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:36:15Z","timestamp":1769693775348,"version":"3.49.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,12,17]],"date-time":"2020-12-17T00:00:00Z","timestamp":1608163200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A tight Hamilton cycle in a <jats:italic>k<\/jats:italic>-uniform hypergraph (<jats:italic>k<\/jats:italic>-graph) <jats:italic>G<\/jats:italic> is a cyclic ordering of the vertices of <jats:italic>G<\/jats:italic> such that every set of <jats:italic>k<\/jats:italic> consecutive vertices in the ordering forms an edge. R\u00f6dl, Ruci\u0144ski and Szemer\u00e9di proved that for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000619_inline1.png\"\/><jats:tex-math>\n$k\\ge 3$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, every <jats:italic>k<\/jats:italic>-graph on <jats:italic>n<\/jats:italic> vertices with minimum codegree at least <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000619_inline2.png\"\/><jats:tex-math>\n$n\/2+o(n)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such <jats:italic>k<\/jats:italic>-graphs is <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000619_inline3.png\"\/><jats:tex-math>\n${\\exp(n\\ln n-\\Theta(n))}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. As a corollary, we obtain a similar estimate on the number of Hamilton <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000619_inline4.png\"\/><jats:tex-math>\n${\\ell}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-cycles in such <jats:italic>k<\/jats:italic>-graphs for all <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000619_inline5.png\"\/><jats:tex-math>\n${\\ell\\in\\{0,\\ldots,k-1\\}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, which makes progress on a question of Ferber, Krivelevich and Sudakov.<\/jats:p>","DOI":"10.1017\/s0963548320000619","type":"journal-article","created":{"date-parts":[[2020,12,17]],"date-time":"2020-12-17T16:25:19Z","timestamp":1608222319000},"page":"631-653","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["Counting Hamilton cycles in Dirac hypergraphs"],"prefix":"10.1017","volume":"30","author":[{"given":"Stefan","family":"Glock","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Gould","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Felix","family":"Joos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniela","family":"K\u00fchn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deryk","family":"Osthus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,12,17]]},"reference":[{"key":"S0963548320000619_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000486"},{"key":"S0963548320000619_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14444-8_16"},{"key":"S0963548320000619_ref9","doi-asserted-by":"crossref","unstructured":"[9] Czygrinow, A. and Molla, T. 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