Climbing Elements in Finite Coxeter Groups

@article{Brady2010ClimbingEI,
  title={Climbing Elements in Finite Coxeter Groups},
  author={Thomas Brady and Aisling Kenny and Colum Watt},
  journal={Electron. J. Comb.},
  year={2010},
  volume={17}
}
We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element. 
View PDF on arXiv

References

SHOWING 1-10 OF 17 REFERENCES
Non-crossing partition lattices in finite real reflection groups
For a finite real reflection group W with Coxeter element γ we give a case-free proof that the closed interval, [I,-γ], forms a lattice in the partial order on W induced by reflection length. Key to…
Sortable elements and Cambrian lattices
Abstract.We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this…
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
Introduction Coxeter groups and noncrossing partitions $k$-divisible noncrossing partitions The classical types Fuss-Catalan combinatorics Bibliography.
From permutahedron to associahedron
  • T. Brady, C. Watt
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2010
Abstract For each finite real reflection group W, we identify a copy of the type-W simplicial generalized associahedron inside the corresponding simplicial permutahedron. This defines a bijection…
Combinatorics of Coxeter Groups
I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial…
A characterization of a special ordering in a root system
We give necessary and sufficient conditions for an ordering of a set of positive roots in a root system R to be associated to a reduced expression of an element of the Weyl group of R . Finally we…
Cambrian fans
For a finite Coxeter group W and a Coxeter element c of W, the c-Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W. Its maximal cones are naturally indexed by the…
Lie groups and Lie algebras
From the reviews of the French edition "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular…
$h$-Vectors of Generalized Associahedra and Noncrossing Partitions
A uniform proof is given that the entries of the hvector of the cluster complex ∆(Φ), associated by S. Fomin and A. Zelevinsky to a finite root system Φ, count elements of the lattice L of…
Combinatorics of Coxeter groups, Graduate Texts in Mathematics
  • Combinatorics of Coxeter groups, Graduate Texts in Mathematics
  • 2005
...
...