##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Anton Mellit

#### International School for Advanced Studies (SISSA) and International Center for Theoretical Physics

## Symmetric functions associated to Dyck paths

##### Abstract:

I will talk about my recent work with Erik Carlsson in which we studied certain symmetric functions associated to Dyck paths. For each Dyck path from (0,0) to (n,n) the corresponding symmetric function is a generating function of labelings of the positions 1,2,...,n by positive integers. Each labeling is counted with a weight which depends on whether labels on positions i,j are in the correct or reversed order and whether (i,j) is above or under the path. While studying these symmetric functions we discovered an interesting algebraic structure that controls them. This ultimately led us to a proof of the shuffle conjecture by Haglund, Haiman, Loehr, Remmel, and Ulyanov.

Host: Jeff Remmel

### February 23, 2016

### 3:00 PM

### AP&M 7321

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