DOI: 10.1017/s0305004126102059 ISSN: 0305-0041
Thresholds for (
n
,
q
, 2)-Steiner systems via refined absorption
MICHELLE DELCOURT, TOM KELLY, LUKE POSTLE 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
$p \geq n^{-(q-6)/2}$
, 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
)
$\mathcal{G}^{(q)}(n,p)$
contains an (
n
,
q
, 2)-Steiner system, provided
n
satisfies the necessary divisibility conditions.