derangement

错排

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

Other names / variants: fixed-point-free permutation

Translation evidence: Literature usage

Meaning in context

A derangement of {1,…,n} is a bijection σ of that set with σ(i) ≠ i for every i. The empty permutation is a derangement by the vacuous convention.

集合 {1,…,n} 的错排是不固定任何元素的自双射；按空条件约定，空置换也算一个错排。

Example

On three positions, (2,3,1)(2,3,1) and (3,1,2)(3,1,2) are the two derangements.

Usage and distinctions

Having at least one moved element is insufficient; every element must move.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 7.4, opening definition, Lemma 7.10 and Theorem 7.11 · Checked 2026-10-14

Translation sources

  1. 上海交通大学 — CS0901 组合数学（2026）课程目录目录，第3讲说明「满射与错排」（名称证据，仅课程目录） · Checked 2026-10-14
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