In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y...In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.展开更多
文摘In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.
