##### Department of Mathematics,

University of California San Diego

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### Special Combinatorics Seminar

## Richard Stanley

#### MIT

## Unimodality and real zeros of P-Eulerian polynomials

##### Abstract:

The $P-$Eulerian polynomial $W_P(x)$ of a finite naturally labelled poset $P$ is the generating function for linear extensions of $P$ by number of descents. We will discuss some recent work related to the question of whether the coefficients of $W_P(x)$ are unimodal and whether $W_P(x)$ has real zeros. In particular we will explain the beautiful work of Branden on sign-graded posets.

Host: Adriano Garsia

### November 15, 2006

### 3:30 PM

### AP&M 6402

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