Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
The character theory of the symmetric group is used to derive properties of the number of permutations, with k cycles, which are expressible as the product of a full cycle with an element of an arbitrary, but fixed, conjugacy class.For the conjugacy class of fixed point free involutions, this problem …