 Growth of the two-variable Laurent polynomial algebra

ID: 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}

Y_{1}^{a} Y_{2}^{b}

with

∣ a ∣ + ∣ b ∣ \leq j

. The number of integer lattice points in this diamond is

1 + 4 \sum_{r = 1}^{j} r = 2 j^{2} + 2 j + 1.

Its quadratic growth agrees with

dim R = 2

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