##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Adriano M. Garsia

#### UCSD

## The Gessel-Reutenauer enumeration of permutations by major index and cycle structure and some of its applications

##### Abstract:

In seminal paper, Gessel-Reutenauer construct a truly remarkable bijection between words in the free monoid over an infinite alphabet and multisets of primitive necklaces. Using this bijection Gessel-Reutenauer derive a variety of beautiful symmetric function identities with deep implications in permutation enumeration. In this talk we review the Gessel-Reutenauer results, derive some applications and state some challenging combinatorial problems.

Host:

### May 24, 2005

### 4:00 PM

### AP&M 7321

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