I don't understand this computation (this is from McCleary's book on spectral sequences, p.15): The Poincare series of a (locally finite) bigraded vector space $E^{\ast,\ast}$ is defined as
$P(E^{\ast,\ast}, t) = \sum_{n=0}^\infty dim(\oplus_{n = p + q} E^{p,q})t^n.$
Then he takes the example where $E^{\ast,\ast} = \mathbb{Q}[x,y,z]/(x^2=y^4=z^2=0)$ and $bideg(x) = (7,1)$, $bideg(y)=(3,0)$ and $bideg(z)=(0,2)$. He then says that the Poincare series for this bigraded vector space is equal to $(1+t^11)(1+t^4 +t^8 +t^12)(1+t^3) = t^{26}+t^{23}+t^{22}+t^{19}+t^{18}+2t^{15}+t^{14}+t^{12}+2 t^{11}+t^{8}+t^{7}+t^{4}+t^3+1.$
But when I try to make the computation myself I don't get the same polynomial. My computation:
total degree p+q | generators
0 | 0
1 | 0
2 | z
3 | y
4 | 0
5 | yz
6 | y^2
7 | 0
8 | x, y^2z
9 | y^3
10 | xz
11 | xy, y^3z
12 | 0
13 | xyz
14 | xy^2
15 | 0
16 | xy^2z
17 | xy^3
18 | 0
19 | xy^3z
The Poincare series I get is $t^2+t^3+t^5+t^6+2t^8+t^9+t^{10}+2t^{11}+t^{13}+t^{14}+t^{16}+t^{16}+t^{19}$