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dc.contributor.authorSah, Ashwin
dc.contributor.authorSawhney, Mehtaab
dc.contributor.authorSimkin, Michael
dc.date.accessioned2023-07-20T17:49:52Z
dc.date.available2023-07-20T17:49:52Z
dc.date.issued2023-06-19
dc.identifier.urihttps://hdl.handle.net/1721.1/151139
dc.description.abstractAbstract We prove that with high probability $$\mathbb {G}^{(3)}(n,n^{-1+o(1)})$$ G ( 3 ) ( n , n - 1 + o ( 1 ) ) contains a spanning Steiner triple system for $$n\equiv 1,3\pmod {6}$$ n ≡ 1 , 3 ( mod 6 ) , establishing the exponent for the threshold probability for existence of a Steiner triple system. We also prove the analogous theorem for Latin squares. Our result follows from a novel bootstrapping scheme that utilizes iterative absorption as well as the connection between thresholds and fractional expectation-thresholds established by Frankston, Kahn, Narayanan, and Park.en_US
dc.publisherSpringer International Publishingen_US
dc.relation.isversionofhttps://doi.org/10.1007/s00039-023-00639-6en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer International Publishingen_US
dc.titleThreshold for Steiner triple systemsen_US
dc.typeArticleen_US
dc.identifier.citationSah, Ashwin, Sawhney, Mehtaab and Simkin, Michael. 2023. "Threshold for Steiner triple systems."
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2023-07-19T03:23:11Z
dc.language.rfc3066en
dc.rights.holderThe Author(s), under exclusive licence to Springer Nature Switzerland AG
dspace.embargo.termsY
dspace.date.submission2023-07-19T03:23:11Z
mit.licensePUBLISHER_POLICY
mit.metadata.statusAuthority Work and Publication Information Neededen_US


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