A multigrade operator $\Omega$ is a parametric operator with parameter $k$ in the set $\mathbb{N}$ 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 $\Omega(x_{1},\ldots,x_{k})$ may be taken for $\Omega_{k}(x_{1},\ldots,x_{k}).$