# Zonotoptes Associated with Higher Bruhat Orders

###
Stefan Felsner

Institut für Informatik

Freie Universität Berlin

Takustr. 9, D-14195 Berlin

email: felsner@inf.fu-berlin.de

Günter M. Ziegler

Fachbereich Mathematik

Technische Universität Berlin

Straße des 17. Juni 136, D-10623 Berlin

email: ziegler@math.tu-berlin.de

Report B 99-04

March 1999

The higher Bruhat orders *B (n, k)* are combinatorially defined partial orders (and hence graphs) that "look like" the graphs of *(n-k)*-dimensional zonotopes - and they are, for small parameters. Here we explain that this is since they *contain* the graphs of zonotopes of this dimension, but that in general they are not covered by these zonotopal graphs, and they are not polytopal in general.

As a special case, this applies to the graph *G*_{n} of all arrangements of *n* pseudolines connected by flips, since this graph is the graph of the higher Bruhat order **B (n, 2).
**

**Get the report here or by anonymous ftp:
Server: fubinf.inf.fu-berlin.de
File: pub/reports/tr-b-99-04.ps.gz
**

**
**