##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Christophe Hohlweg

#### York Univeristy and Fields Insititute

## Realizations of the associahedron and cyclohedron

##### Abstract:

Abstract: We describe different realizations with integer coordinates for the associahedron (i.e., the Stasheff polytope) and for the cyclohedron (i.e., the Bott-Taubes polytope), and compare them to the permutahedra of type A and B, respectively. The coordinates are integral and obtained by an algorithm which uses an oriented Coxeter graph of type A or B respectively as the only input and which specializes to a procedure presented by J.-L. Loday for a certain orientation of the Coxeter graph of An. The described realizations have cambrian fans of type A and B as normal fans. This settles a conjecture of N. Reading for cambrian fans of these types. This is a joint work with Carsten Lange

Host: Jeff Remmel

### April 25, 2006

### 4:00 PM

### AP&M 7321

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