{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T09:19:02Z","timestamp":1773825542602,"version":"3.50.1"},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T00:00:00Z","timestamp":1717027200000},"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":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a simple method to estimate the number of distinct copies of some classes of spanning subgraphs in hypergraphs with a high minimum degree. In particular, for each <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline1.png\"\/><jats:tex-math>\n$k\\geq 2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline2.png\"\/><jats:tex-math>\n$1\\leq \\ell \\leq k-1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, we show that every <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline3.png\"\/><jats:tex-math>\n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-graph on <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline4.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> vertices with minimum codegree at least<jats:disp-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" mimetype=\"image\" position=\"float\" xlink:href=\"S0963548324000178_eqnU1.png\"\/><jats:tex-math>\n\\begin{equation*} \\left \\{\\begin {array}{l@{\\quad}l} \\left (\\dfrac {1}{2}+o(1)\\right )n &amp; \\text { if }(k-\\ell )\\mid k,\\\\[5pt] \\left (\\dfrac {1}{\\lceil \\frac {k}{k-\\ell }\\rceil (k-\\ell )}+o(1)\\right )n &amp; \\text { if }(k-\\ell )\\nmid k, \\end {array} \\right . \\end{equation*}\n<\/jats:tex-math><\/jats:alternatives><\/jats:disp-formula>contains <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline5.png\"\/><jats:tex-math>\n$\\exp\\!(n\\log n-\\Theta (n))$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> Hamilton <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline6.png\"\/><jats:tex-math>\n$\\ell$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-cycles as long as <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline7.png\"\/><jats:tex-math>\n$(k-\\ell )\\mid n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. When <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline8.png\"\/><jats:tex-math>\n$(k-\\ell )\\mid k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, this gives a simple proof of a result of Glock, Gould, Joos, K\u00fchn, and Osthus, while when <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline9.png\"\/><jats:tex-math>\n$(k-\\ell )\\nmid k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, this gives a weaker count than that given by Ferber, Hardiman, and Mond, or when <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000178_inline10.png\"\/><jats:tex-math>\n$\\ell \\lt k\/2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, by Ferber, Krivelevich, and Sudakov, but one that holds for an asymptotically optimal minimum codegree bound.<\/jats:p>","DOI":"10.1017\/s0963548324000178","type":"journal-article","created":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T04:00:09Z","timestamp":1717041609000},"page":"729-741","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Counting spanning subgraphs in dense hypergraphs"],"prefix":"10.1017","volume":"33","author":[{"given":"Richard","family":"Montgomery","sequence":"first","affiliation":[]},{"given":"Mat\u00edas","family":"Pavez-Sign\u00e9","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,5,30]]},"reference":[{"key":"S0963548324000178_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13580-4_5"},{"key":"S0963548324000178_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301004849"},{"key":"S0963548324000178_ref4","first-page":"1231","volume-title":"Handbook of combinatorics","author":"Bolob\u00e1s","year":"1995"},{"key":"S0963548324000178_ref27","first-page":"381","volume-title":"2014 International Congress of Mathematicians, ICM","author":"K\u00fchn","year":"2014"},{"key":"S0963548324000178_ref5","first-page":"3","volume-title":"Handbook of combinatorics","author":"Bondy","year":"1995"},{"key":"S0963548324000178_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2010.02.010"},{"key":"S0963548324000178_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2015.09.032"},{"key":"S0963548324000178_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107359949.008"},{"key":"S0963548324000178_ref10","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548324000178_ref12","first-page":"135","article-title":"Counting and packing Hamilton \n\n\n\n$\\ell$\n\n\n-cycles in dense hypergraphs","volume":"7","author":"Ferber","year":"2016","journal-title":"J Comb"},{"key":"S0963548324000178_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001012"},{"key":"S0963548324000178_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001620"},{"key":"S0963548324000178_ref23","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199811)29:3<167::AID-JGT4>3.0.CO;2-O"},{"key":"S0963548324000178_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2360-2"},{"key":"S0963548324000178_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2254-3"},{"key":"S0963548324000178_ref1","unstructured":"[1] Allen, P. , B\u00f6ttcher, J. , Corsten, J. , Davies, E. , Jenssen, M. , Morris, P. , Roberts, B. and Skokan, J. 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