Abstract
For a finite real reflection group, $W$, with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the construction of a simplicial complex which can be embedded in the type W simplicial generalised associahedron.
Original language | English |
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Journal | arXiv: Combinatorics |
DOIs | |
Publication status | Published - 1 Jan 2008 |
Keywords
- finite real reflection group
- Coxeter element
- lattice
- partial order
- reflection length
- simplicial complex
- generalised associahedron