##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Allen Knutson

#### UCSD

## Tableau Complexes

##### Abstract:

Let $T$ be a collection of functions from $X$ to $Y$, and call them ``tableaux". I'll describe a simplicial complex whose facets correspond exactly to these tableaux, with many good properties. \vskip .1in \noindent Something particularly nice happens if $X$ is a poset, $Y$ is totally ordered, and the tableaux are weakly order-preserving functions; then the simplicial complex is homeomorphic to a ball. (This is a sign of an interesting complex, and I'll recall why.) \vskip .1in \noindent This work is joint with Ezra Miller and Alex Yong (both in Minnesota).

Host:

### October 11, 2005

### 4:00 PM

### AP&M 7321

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