##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Martha Yip

#### UCSD

## Macdonald polynomials, parking functions, trees, and zonotopal algebras

##### Abstract:

These objects are related to each other through their connection to the Shi hyperplane arrangement. We will give definitions of each of these objects, and through six bijections, show how the basis for a Gordon module consisting of Macdonald polynomials is connected to the basis for the central space of a zonotopal algebra. We will also see Catalan numbers appear in this story of six bijections.

Host: Jeff Remmel

### October 19, 2010

### 4:00 PM

### AP&M 7321

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