Symmetric multilinear forms and polarization of polynomials

Abstract

We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in more variables. The main tool is combinatorial polarization, and the approach is applicable even when the factorial of the number of variables is not invertible in the underlying field.

Keywords

• Symmetric
• multilinear
• forms
• polarization
• polynomials