##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Jason Bandlow

#### UCSD Graduate Student

## $q,t$-Analogs of multinomial coefficients indexed by lattice diagrams

##### Abstract:

The MacDonald polynomials have long been a source of interesting combinatorial questions. In a recent paper, Haglund, Haiman and Loeher managed to give an entirely combinatorial description of them. They showed that their description defines polynomials indexed not just by partitions, but indeed by any diagram of cells in the positive integer lattice. However, the combinatorial coefficients they describe are somewhat unwieldly. I will show how these coefficients can be expressed as certain $q,t$ analogs of multinomial coefficients, and give a recursive construction for rectangular shapes.

Host:

### October 18, 2005

### 4:00 PM

### AP&M 7321

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