MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $C_n$ be the cyclic group of order $n$ acting on a finite set $X$ and let $Z(C_n, X; p_1,p_2,\dots)$ be the cycle index of the corresponding permutation group.

I wonder whether the knowledge of the cycle index alone is enough to determine the number of fixed points of the action of a given element $g\in C_n$ on $X$?

share|cite|improve this question
Yes; fixed points are cycles of length 1. – Qiaochu Yuan Feb 16 '11 at 14:12
Thank's, I missed the obvious. – Martin Rubey Feb 16 '11 at 14:57

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.