Packing polynomials on irrational sectors

Article Type

Research Article

Publication Title

Research in Number Theory


Fueter and Polya proved that the only quadratic polynomials giving a bijection between N and N2 are the two Cantor polynomials. It is conjectured that there is no bijection from N2 onto N given by a polynomial of degree at least 3. A similar problem arises when the domain of the map is replaced by the set of integral points in some sector in R2. Rational sectors were considered by Nathanson and Stanton. Here, we study and solve the case of general irrational sectors. In fact, our method enables us also to recover the results on rational sectors and also answer a question posed by Nathanson.



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