Definition:Multigrade Operator

Definition
A multigrade operator $\Omega$ is a parametric operator with parameter $k$ in the set $\N$ of non-negative integers.

The application of a multigrade operator $\Omega$ to a finite sequence of operands $(x_1, \ldots, x_k)$ is typically denoted with the parameter $k$ left tacit, as the appropriate application is implicit in the number of operands listed.

Thus $\Omega (x_1, \ldots, x_k)$ is taken to mean $\Omega_k (x_1, \ldots, x_k)$.