##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Gene Kim

#### University of Southern California

## Distribution of descents in matchings and derangements

##### Abstract:

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 and uses a generating function approach to prove a central limit theorem for the number of descents in matchings. We also extend this result to derangements.

Host: Brendon Rhoades

### March 13, 2018

### 4:00 PM

### AP&M 7321

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