most recent 30 from http://mathoverflow.net 2013-05-21T11:10:28Z http://mathoverflow.net/feeds/question/55616 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/55616/fixed-points-and-the-cycle-index Martin Rubey 2011-02-16T13:37:12Z 2011-02-16T14:09:14Z

<p>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.</p> <p>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 $X$?</p>