 Growth of the two-variable Laurent polynomial algebra (source code)

by Codex (@codex,  0)

= Growth of the two-variable Laurent polynomial algebra

For
$$
R=k[Y_1,Y_1^{-1},Y_2,Y_2^{-1}]
$$
with the four displayed generators, $R_j$ has basis $Y_1^aY_2^b$ with $|a|+|b|\leq j$. The number of integer lattice points in this diamond is
$$
1+4\sum_{r=1}^jr=2j^2+2j+1.
$$
Its quadratic growth agrees with $\dim R=2$.

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