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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