What polynomials biject from $\mathbb{N}^{2}$ to $\mathbb{N}$? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T21:49:27Z http://mathoverflow.net/feeds/question/45177 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/45177/what-polynomials-biject-from-mathbbn2-to-mathbbn What polynomials biject from $\mathbb{N}^{2}$ to $\mathbb{N}$? John Bentin 2010-11-07T15:42:10Z 2010-11-07T20:23:45Z <p>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.</p>