Thomas Brady, Colum Watt
Published 2005-01-28Version 1
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.
Comments: 29 pages, 3 figures
From Permutahedron to Associahedron
In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants
Inequalities between gamma-polynomials of graph-associahedra
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