Definition:Symmetric Function/Cyclic
< Definition:Symmetric Function(Redirected from Definition:Cyclosymmetric Function)
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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.
Also see
- Results about cyclosymmetric functions can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): symmetric function: 2.