On Polynomially Normal Lattice Configurations

摘要

In this paper we extend Champernowne’s construction of a normal sequence in base b to the ${Bbb N}^2$ case and obtain an explicit construction of the generic point of the ${Bbb N}^2$ shift transformation of the set ${0,1,ldots,b-1}^{{Bbb N}^2}$ . We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal sequence in base b.