##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Sean Griffin

#### University of Washington

## Labeled binary trees, sub arrangements of the Catalan arrangements, and Schur-positiity

##### Abstract:

In 1995, Gessel introduced a multivariate formal power series $G$ tracking the distribution of ascents and descents in labeled binary trees. In addition to showing the $G$ is a symmetric function, he conjectured that $G$ is Schur-positive. In this talk, we'll see how to expand $G$ positively in terms of ribbon Schur functions. Moreover, we'll see how certain specializations of $G$ relate to actions on hyperplane arrangements. As an application of our work, we get a proof of gamma-positivity of the distribution of right edges over the set of local binary search trees.

Host: Brendon Rhoades

### May 14, 2019

### 2:00 PM

### AP&M 7321

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