I’ve added a new page of reading recommendations, mostly for undergraduates, to the top. The emphasis is intended to be on well-written and accessible books. Comments and suggestions welcome.
Archive for July, 2013
The goal of this post is to collect a list of applications of the following theorem, which is perhaps the simplest example of a fixed point theorem.
Theorem: Let be a finite -group acting on a finite set . Let denote the subset of consisting of those elements fixed by . Then ; in particular, if then has a fixed point.
Although this theorem is an elementary exercise, it has a surprising number of fundamental corollaries.