Gene Kim, University of Southern California
PDL C-401
The distribution of descents in certain conjugacy classes of \$S_n\$ have been previously studied, and it is shown that its moments have interesting properties. This talk provides a bijective proof of the symmetry of the descents and major indices of matchings (also known as fixed point free involutions) and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings. We then generalize this result to fixed point free permutations, and we further extend this result to all conjugacy classes of \$S_n\$.