Probability Seminar presents "Distribution of descents (and other permutation statistics) in conjugacy classes of S_n"
The distribution of descents in Sn, the symmetric group, have been previously studied. This talk starts with a bijective proof (using tableaux) of the symmetry of the descents and major indices in matchings (fixed point free involutions) and uses a generating function approach to prove a central theorem for descents in matchings. This approach will be extended to prove central limit theorems for descents in all conjugacy classes of Sn, and to other permutation statistics, such as peaks and major indices.
This is joint work with Sangchul Lee (UCLA) and should be accessible to all graduate students.