Further results on homogeneous Gröbner bases under composition

Polynomial composition is the operation of replacing variables in a polynomial by other polynomials. This paper studies when Gröbner bases remain Gröbner bases under composition with respect to any fixed term ordering. A complete characterization is given for homogeneous Gröbner bases under an arbitrary grading. This unifies the results of Hong (1998) and Liu and Wang (2006).