Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption

Luke Postle; Michelle Delcourt; Tom Kelly

Thresholds for $(n,q,2)$-Steiner Systems via Refined Absorption

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arxiv 2402.17858 v1 pith:4IER6ON5 submitted 2024-02-27 math.CO

Michelle Delcourt , Tom Kelly , Luke Postle This is my paper

classification math.CO

keywords steinerabsorptionalmostasymptoticallybinomialconditionscontainsdivisibility

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abstract

We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions.

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