Homogeneous Sagbi Bases Under Polynomial Composition

Abstract

The process of replacing indeterminates in a Polynomial with other polynomials is the polynomial composition. Homogeneous Sagbi bases are the Sagbi bases generated by the subset of homogeneous polynomials. In this article, we present adequate and essential criterion on a set of polynomials to guarantee that the composed set S • is Homogeneous Sagbi basis whenever S is a Homogeneous Sagbi basis.