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词汇 Combinatorial methods
分类 英语词汇 英语翻译词典
释义

Combinatorial methods

英语百科

Combinatorial principles

(重定向自Combinatorial methods)
Inclusion–exclusion illustrated for three sets

In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used.

The rule of sum, rule of product, and inclusion-exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements. The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a discrete context. Many combinatorial identities arise from double counting methods or the method of distinguished element. Generating functions and recurrence relations are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations.

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