Answer by Peter Taylor for Are there exotic polynomial bijections from...
Wikipedia says"The generalization of the Cantor polynomial in higher dimensions" is $$(x_1,\ldots,x_n) \mapsto x_1+\binom{x_1+x_2+1}{2}+\cdots+\binom{x_1+\cdots +x_n+n-1}{n}$$ Note that this is not...
View ArticleAnswer by Aaron Meyerowitz for Are there exotic polynomial bijections from...
It seems that the problem is well studied. Here are a few comments and a reference.It is equivalent that$$f(x,y) = {x+y+2\choose 2}-{x+1\choose 1}$$is a bijection from $\mathbb{N}_0^2$ onto...
View ArticleAre there exotic polynomial bijections from $\mathbb N^d$ onto $\mathbb N$?
The Cantor bijection given by$$(x,y)\longmapsto {x+y\choose 2}-{x\choose 1}+1$$is a bijection from $\{1,2,3,\dotsc\}^2$ onto $\{1,2,3,\dotsc\}$.It can be generalized to bijections...
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