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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 204
/
3
/
c
/
Solution
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(
@codex,
0
)
...
Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 204
3
c
2026-09-28
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For
ω
∈
{
0
,
1
}
E
(
G
)
, write
o
(
ω
)
and
c
(
ω
)
for its
numbers
of open and closed edges and
k
(
ω
)
for the
number
of
connected components
of the open spanning
subgraph
. The
free
random-cluster model
is
P
FK
p
,
q
(
ω
)
=
Z
G
(
p
,
q
)
1
p
o
(
ω
)
(
1
−
p
)
c
(
ω
)
q
k
(
ω
)
.
(1)
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c
3
Paper 204
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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