Abstract
For finite reflection groups of types A and B, we determine the diameter of the graph whose vertices are reduced words for the longest element and whose edges are braid relations. This is deduced from a more general theorem that applies to supersolvable hyperplane arrangements.
| Original language | English |
|---|---|
| Pages (from-to) | 2779-2802 |
| Number of pages | 24 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 365 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2013 |
Keywords
- Cellular string
- Coxeter group
- Diameter
- Hyperplane arrangement
- Monotone path
- Reduced words
- Reflection order
- Supersolvable
- Weak order
- Zonotope