▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Empty map
▾ J-tuple
▾ J-tuple-argued-valued map
▾ J-tuple-argued map
▾ Sequence-argued map
▾ Finite sequence-argued map
Symmetric map
Formulation 0
Let $S_N$ be a D1607: Set of permutations on N letters.
Let $X$ be a D11: Set such that
(i) $X^N : = \prod_{n = 1}^N X$ is a D326: Cartesian product
(ii) $f : X^N \to Y$ is a D18: Map
Then $f$ is a symmetric map if and only if \begin{equation} \forall \, \pi \in S_N : \forall \, (x_1, \ldots, x_N) \in X^N : f(x_1, \ldots, x_N) = f(x_{\pi(1)}, \ldots, x_{\pi(N)}) \end{equation}
Child definitions
» D729: Conjugate symmetric complex function
Results
» R5624: Euclidean real dot product is symmetric