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Peer-reviewedCC BYMathematical Proceedings of the Cambridge Philosophical Society

Thresholds for ( n , q , 2)-Steiner systems via refined absorption

  • Michelle Delcourt1
  • Tom Kelly2
  • Luke Postle3
  1. 1Toronto Metropolitan University
  2. 2Georgia Institute of Technology
  3. 3University of Waterloo
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Abstract

We prove that if p greater than or equals n Superscript minus left parenthesis q minus 6 right parenthesis divided by 2 p ≥ n − ( q − 6 ) / 2 p ≥ n−(q−6)/2 , then asymptotically almost surely the binomial random q -uniform hypergraph script upper G Superscript left parenthesis q right parenthesis Baseline left parenthesis n comma p right parenthesis G ( q ) ( n , p ) 𝒢(q)(n,p) contains an ( n , q , 2)-Steiner system, provided n satisfies the necessary divisibility conditions.

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Cite

BibTeXRIS
BibTeX
@article{delcourt2026thresholds,
  title = {{Thresholds for ( n , q , 2)-Steiner systems via refined absorption}},
  author = {Michelle Delcourt and Tom Kelly and Luke Postle},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  year = {2026},
  month = jun,
  doi = {10.1017/s0305004126102059},
  url = {https://doi.org/10.1017/s0305004126102059},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Thresholds for ( n , q , 2)-Steiner systems via refined absorption
AU  - Michelle Delcourt
AU  - Tom Kelly
AU  - Luke Postle
PY  - 2026
DA  - 2026/06/19
JO  - Mathematical Proceedings of the Cambridge Philosophical Society
DO  - 10.1017/s0305004126102059
UR  - https://doi.org/10.1017/s0305004126102059
AB  - We prove that if p greater than or equals n Superscript minus left parenthesis q minus 6 right parenthesis divided by 2 p ≥ n − ( q − 6 ) / 2 p ≥ n^−(q−6)/2 , then asymptotically almost surely the binomial random q -uniform hypergraph script upper G Superscript left parenthesis q right parenthesis Baseline left parenthesis n comma p right parenthesis G ( q ) ( n , p ) 𝒢^(q)(n,p) contains an ( n , q , 2)-Steiner system, provided n satisfies the necessary divisibility conditions.
SN  - 0305-0041
SN  - 1469-8064
ER  -