##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adriano Garsia

#### UCSD

## On the eigenspaces of the random to top operator

##### Abstract:

The Random to top operator $Tn$ is the sum of the cycles ($i,i+1,..n$) for $i=1..n$. This operator has occurred in various contexts that range from algebraic geometry to statistics. It has played a crucial role in the proof of several recent results. In this lecture we completely determine its action in the regular representation of $Sn$.

Host:

### October 4, 2005

### 4:00 PM

### AP&M 7321

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