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 |
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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