pigeonhole principle

鸽巢原理

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

Translation evidence: Literature usage

Meaning in context

If n objects are assigned to m ≥ 1 categories, at least one category contains at least the ceiling of n/m objects; in particular n>m forces a repeated category.

将 n 个对象分入 m≥1 个类别，至少一类含有不少于 n/m 向上取整个对象；特别地，n>m 时必有一类至少含两个对象。

Example

Among nine integers, at least three have the same residue modulo four.

Usage and distinctions

The claim guarantees some category, not any designated category; distinct objects may have identical values.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Joy Morris — Combinatorics, version 2.1.1Section 10.1, generalized pigeonhole principle and discussion preceding Proposition 10.1.8 · Checked 2026-10-14

Translation sources

1. 湖南大学数学学院 — 组合数学课程介绍教学目的和要求「鸽巢原理」；教学内容（六）「鸽巢原理和Ramsey定理」 · Checked 2026-10-14

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