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Shearer trace inequality
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Mathematics
Area of mathematics
Combinatorics
Extremal set theory
Set family
Trace of a set family
2026-09-28
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If every ground element belongs to at least
t
members of
a
family
F
⊆
P
([
n
])
, then
∣
A
∣
≤
(
∏
F
∈
F
∣
T
F
(
A
)
∣
)
1/
t
.
(1)
Apply
Shearer's inequality
to the characteristic
vector
of
a
uniformly random member of
A
.
Ancestors
(7)
Trace of a set family
Set family
Extremal set theory
Combinatorics
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 161
/
2
/
iii
/
Solution
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