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Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 160
/
3
/
a
/
ii
/
Solution
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2023
iii
Paper 160
3
a
ii
2026-09-28
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For
λ
=
(
6
,
5
,
3
)
use the three-bead
beta set
{
8
,
6
,
3
}
. Its runners give the
3-
quotient of a partition
Q
3
(
λ
)
=
(
(
1
,
1
)
,
∅
,
(
2
)
)
.
(1)
The hook
lengths
divisible by three and their
images
are
f
(
H
1
,
3
(
λ
))
f
(
H
1
,
5
(
λ
))
f
(
H
2
,
1
(
λ
))
f
(
H
3
,
1
(
λ
))
=
H
1
,
1
(
λ
(
2
)
)
,
=
H
1
,
2
(
λ
(
2
)
)
,
=
H
1
,
1
(
λ
(
0
)
)
,
=
H
2
,
1
(
λ
(
0
)
)
,
6
3
6
3
=
3
⋅
2
,
=
3
⋅
1
,
=
3
⋅
2
,
=
3
⋅
1.
(2)
There are no others,
as
the complete hook-
length
rows are
(
8
,
7
,
6
,
4
,
3
,
1
)
,
(
6
,
5
,
4
,
2
,
1
)
, and
(
3
,
2
,
1
)
.
Ancestors
(12)
ii
a
3
Paper 160
iii
2023
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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