Definition:Symmetric Function/Cyclic

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Definition

Let $f: \R^n \to \R$ be a real-valued function.

Let $f$ be such that, for all $\mathbf x := \tuple {x_1, x_2, \ldots, x_n} \in \R^n$:

$\map f {\mathbf x} = \map f {\mathbf y}$

where $\mathbf y$ is a cyclic permutation of $\tuple {x_1, x_2, \ldots, x_n}$.

Then $f$ is a cyclosymmetric function.


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