On discriminant-like polynomials (Q1070284)

The authors studies the homogeneous polynomials \(p(x_ 1,...,x_ n)\) with the property \(p(x_ 1+1,...,x_ n+1)=p(x_ 1,...,x_ n)\), the coefficient ring being a field of characteristic zero. A standard example of such a polynomial is the discriminant of a polynomial in one indeterminate. Many interesting properties are established for polynomials which satisfy the above property and two additional conditions. The proofs use linear algebra methods. The paper includes several consistent examples.