Threshold for Steiner triple systems
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39_2023_639_ReferencePDF.pdf
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609.84 KB
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Author(s)
Sah, Ashwin
Sawhney, Mehtaab
Simkin, Michael
Date Issued
June 19, 2023
Publisher
Springer International Publishing
Citation
Sah, Ashwin, Sawhney, Mehtaab and Simkin, Michael. 2023. "Threshold for Steiner triple systems."
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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DOI of Published Version
https://doi.org/10.1007/s00039-023-00639-6
