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Growth of the two-variable Laurent polynomial algebra
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)
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Commutative algebra
Ring
Graded ring
Hilbert series
Hilbert-Serre theorem
Growth of a finitely generated commutative algebra
2026-10-03
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For
R
=
k
[
Y
1
,
Y
1
−
1
,
Y
2
,
Y
2
−
1
]
(1)
with the four displayed generators,
R
j
has
basis
Y
1
a
Y
2
b
with
∣
a
∣
+
∣
b
∣
≤
j
. The
number
of
integer lattice
points in this
diamond
is
1
+
4
∑
r
=
1
j
r
=
2
j
2
+
2
j
+
1.
(2)
Its
quadratic growth
agrees with
dim
R
=
2
.
Ancestors
(10)
Growth of a finitely generated commutative algebra
Hilbert-Serre theorem
Hilbert series
Graded ring
Ring
Commutative algebra
Algebra
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 148
/
6
/
Solution
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