permutation of a finite set

排列

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: full permutation

Translation evidence: Literature usage

Meaning in context

A permutation of a finite set X is an ordering of all its elements, equivalently a bijection from {1,…,|X|} to X. An n-element set has n! such orderings, including one empty ordering when n=0.

有限集合 X 的排列是其全部元素的一种顺序，也可看成从 {1,…,|X|} 到 X 的双射；空集有一个空排列。

Example

The order $(c,a,b)$ is one permutation of $\{a,b,c\}$.

Usage and distinctions

This record uses full orderings; some counting texts also call shorter injective strings permutations. A self-bijection requires a chosen identification with positions.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Keller and Trotter — Applied Combinatorics (2016)Section 2.2, definition of an X-permutation · Checked 2026-10-14

Translation sources

1. 上海交通大学 — CS0901 组合数学（2026）§2.4，例2.14「排列」 · Checked 2026-10-14

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