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A symmetric function is a function which is unchanged under any permutation of its variables, for example:

$$f(x,y,z) = x^2+y^2+z^2+xy+xz+yz$$

There are sets of functions in which the individual functions are not symmetric but the set as a whole is unchanged under any permutation of the variables in the functions. An example is the set comprising the following three functions:

$$f(x,y,z) = x^2 + yz$$ $$g(x,y,z) = y^2 + xz$$ $$h(x,y,z) = z^2 + xy$$

Is there a term for such a set of functions?

Adam Bailey
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1 Answers1

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I don't think there is a standard term for that property, but invariant set seems clear enough.

lhf
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  • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review – Klangen Jul 29 '19 at 11:58
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    @Klangen From my perspective as the OP it is quite helpful to know that a high-rep user thinks there is no standard term for the property. It reassures me that my failure to find such a term from my own searching was not just because I was looking in the wrong places. – Adam Bailey Jul 29 '19 at 21:11