{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T22:33:55Z","timestamp":1771022035018,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T00:00:00Z","timestamp":1728518400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We use Stein\u2019s method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and multi-variate Poisson approximations to the counts of cycles and normal approximations to the counts of unicyclic subgraphs; we also give a partial result for the counts of trees. We further find a class of multicyclic graphs whose subgraph counts are a.s. bounded as <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000294_inline1.png\"\/><jats:tex-math>\n$n\\to \\infty$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0963548324000294","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T12:56:55Z","timestamp":1728565015000},"page":"90-114","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Approximation of subgraph counts in the uniform attachment model"],"prefix":"10.1017","volume":"34","author":[{"given":"Johan","family":"Bj\u00f6rklund","sequence":"first","affiliation":[]},{"given":"Cecilia","family":"Holmgren","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9680-2790","authenticated-orcid":false,"given":"Svante","family":"Janson","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4762-8914","authenticated-orcid":false,"given":"Tiffany Y. Y.","family":"Lo","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,10,10]]},"reference":[{"key":"S0963548324000294_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/3215259"},{"key":"S0963548324000294_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s11512-009-0118-0"},{"key":"S0963548324000294_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240070102"},{"key":"S0963548324000294_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548312000260"},{"key":"S0963548324000294_ref9","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1269610825"},{"key":"S0963548324000294_ref8","volume-title":"An Introduction to Probability Theory and its Applications","author":"Feller","year":"1971"},{"key":"S0963548324000294_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/11-PS182"},{"key":"S0963548324000294_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.21195"},{"key":"S0963548324000294_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S096354839900382X"},{"key":"S0963548324000294_ref10","doi-asserted-by":"publisher","DOI":"10.1137\/060653950"},{"key":"S0963548324000294_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-211-75357-6"},{"key":"S0963548324000294_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198522355.001.0001"},{"key":"S0963548324000294_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15007-4"},{"key":"S0963548324000294_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61680-2_57"},{"key":"S0963548324000294_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v20-3627"},{"key":"S0963548324000294_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(70)90071-4"},{"key":"S0963548324000294_ref15","volume-title":"The Art of Computer Programming","author":"Knuth","year":"1997"},{"key":"S0963548324000294_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0044-4"},{"key":"S0963548324000294_ref11","first-page":"661","article-title":"Subtree sizes in recursive trees and binary search trees: Berry\u2013Esseen bounds and Poisson approximations","volume":"17","author":"Fuchs","year":"2008","journal-title":"Comb. Prob. Comp."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000294","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T09:51:29Z","timestamp":1740390689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000294\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,10]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["S0963548324000294"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000294","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,10]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the same Creative Commons licence is included and the original work is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}