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# What polynomials biject from \mathbb{N}^{2}$\mathbb{N}^{2}$ to \mathbb{N}?$\mathbb{N}$?
Perhaps there are none with integral coefficients; so let us admit rational coefficients. The map $(x, y) \mapsto x + \frac{1}{2}(x + y)(x + y + 1)$ is well known, and swapping $x$ and $y$ in the formula yields another, so we have two for starters.