{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T14:15:17Z","timestamp":1774880117051,"version":"3.50.1"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000},"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":[[2023,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We find an asymptotic enumeration formula for the number of simple <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000190_inline1.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations. We give sufficient conditions on the degree sequence which guarantee existence of a solution to this system. Furthermore, we solve the system and give an explicit asymptotic formula when the degree sequence is close to regular. This allows us to establish several properties of the degree sequence of a random <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000190_inline2.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-uniform hypergraph with a given number of edges. More specifically, we compare the degree sequence of a random <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000190_inline3.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-uniform hypergraph with a given number edges to certain models involving sequences of binomial or hypergeometric random variables conditioned on their sum.<\/jats:p>","DOI":"10.1017\/s0963548322000190","type":"journal-article","created":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T04:38:02Z","timestamp":1660538282000},"page":"183-224","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Degree sequences of sufficiently dense random uniform hypergraphs"],"prefix":"10.1017","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6998-2282","authenticated-orcid":false,"given":"Catherine","family":"Greenhill","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5703-0951","authenticated-orcid":false,"given":"Mikhail","family":"Isaev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3792-3701","authenticated-orcid":false,"given":"Tam\u00e1s","family":"Makai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3553-0496","authenticated-orcid":false,"given":"Brendan D.","family":"McKay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,8,15]]},"reference":[{"key":"S0963548322000190_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2015.06.004"},{"key":"S0963548322000190_ref18","unstructured":"[18] Liebenau, A. and Wormald, N. (2017) Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph, Preprint, 2017. arXiv:1702.08373."},{"key":"S0963548322000190_ref11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"S0963548322000190_ref3","doi-asserted-by":"publisher","DOI":"10.37236\/5512"},{"key":"S0963548322000190_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-009-9768-3"},{"key":"S0963548322000190_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"S0963548322000190_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2013.07.018"},{"key":"S0963548322000190_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20970"},{"key":"S0963548322000190_ref6","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP728"},{"key":"S0963548322000190_ref22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719512"},{"key":"S0963548322000190_ref29","first-page":"3263","volume-title":"Proceedings of the International Congress of Mathematicians, ICM 2018","volume":"4","author":"Wormald","year":"2018"},{"key":"S0963548322000190_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2007.03.009"},{"key":"S0963548322000190_ref19","article-title":"Asymptotic enumeration of digraphs and bipartite graphs by degree sequence","author":"Liebenau","journal-title":"Random Struct. 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