dc.contributor.author | Sah, Ashwin | |
dc.contributor.author | Sawhney, Mehtaab | |
dc.contributor.author | Simkin, Michael | |
dc.date.accessioned | 2023-07-20T17:49:52Z | |
dc.date.available | 2023-07-20T17:49:52Z | |
dc.date.issued | 2023-06-19 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/151139 | |
dc.description.abstract | Abstract
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.publisher | Springer International Publishing | en_US |
dc.relation.isversionof | https://doi.org/10.1007/s00039-023-00639-6 | en_US |
dc.rights | Article 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.source | Springer International Publishing | en_US |
dc.title | Threshold for Steiner triple systems | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Sah, Ashwin, Sawhney, Mehtaab and Simkin, Michael. 2023. "Threshold for Steiner triple systems." | |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2023-07-19T03:23:11Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | The Author(s), under exclusive licence to Springer Nature Switzerland AG | |
dspace.embargo.terms | Y | |
dspace.date.submission | 2023-07-19T03:23:11Z | |
mit.license | PUBLISHER_POLICY | |
mit.metadata.status | Authority Work and Publication Information Needed | en_US |