Definition:Symmetric Mapping (Mapping Theory)
Jump to navigation
Jump to search
Definition
Let $n \in \N$ be a natural number.
Let $S^n$ be an $n$-dimensional cartesian space on a set $S$.
Let $f: S^n \to T$ be a mapping from $S^n$ to a set $T$.
Then $f$ is a symmetric mapping if and only if:
- $\map f {x_1, x_2, \dotsc, x_n} = \map f {x_{\map \pi 1}, x_{\map \pi 2}, \dotsc x_{\map \pi n} }$
for all permutations $\pi$ on $\set {1, 2, \dotsc n}$.
That is, a symmetric mapping is a mapping defined on a cartesian space whose values are preserved under permutation of its arguments.
Sources
- 1988: Dominic Welsh: Codes and Cryptography ... (previous) ... (next): $\S 1$: Entropy = uncertainty = information: $1.1$ Uncertainty