Multigrade operator

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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 $\Omega_k (x_1, \ldots, x_k).\!$

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