请输入您要查询的字词:

 

单词 ProofOfCountingTheorem
释义

proof of counting theorem


Let N be the cardinality of the set of all the couples (g,x) such that gx=x. For each gG, there exist stabg(X) couples with g as the first element, while for each x, there are |Gx| couples with x as the second element. Hence the following equality holds:

N=gGstabg(X)=xX|Gx|.

From the orbit-stabilizer theorem it follows that:

N=|G|xX1|G(x)|.

Since all the x belonging to the same orbit G(x) contribute with

|G(x)|1|G(x)|=1

in the sum, then xX1/|G(x)| precisely equals the number of distinct orbits s. We have therefore

gGstabg(X)=|G|s,

which proves the theorem.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 19:29:46