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Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

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 $c$ -sortable elements of $W$ . The main result of this paper is that the known bijection cl $_{c}$ between $c$ -sortable elements and $c$ -clusters induces a combinatorial isomorphism of fans. In particular, the $c$ -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for $W$ . The rays...

Castles in the Air Revisited.

M. Sharir, B. Aronov (1994)

Discrete & computational geometry

Cochain operations and subspace arrangements.

Klaus, Stephan (2003)

Portugaliae Mathematica. Nova Série

Colored partitions and a generalization of the braid arrangement.

Welker, Volkmar (1997)

The Electronic Journal of Combinatorics [electronic only]

Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.

H. Edelsbrunner, E. Welzl, L.J. Guibas, K.L. Clarkson, M. Sharir (1990)

Discrete & computational geometry

Combinatorial Models for the Finite-Dimensional Grassmannians.

G.M. Ziegler, T.H. Brylawski (1993)

Discrete & computational geometry

Combinatorial topology and the global dimension of algebras arising in combinatorics

Stuart Margolis, Franco Saliola, Benjamin Steinberg (2015)

Journal of the European Mathematical Society

In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid structure on the set of faces. This theory was later extended by Brown to a larger class of monoids called left regular bands. In both cases, the representation theory of these monoids played a prominent role. In particular, it was used to compute the spectrum of the...

Counting Facets and Incidences.

P.K. Agarwal, B. Aronov (1992)

Discrete & computational geometry

Coxeter group actions on the complement of hyperplanes and special involutions

Giovanni Felder, A. Veselov (2005)

Journal of the European Mathematical Society

We consider both standard and twisted actions of a (real) Coxeter group $G$ on the complement $ℳ_{G}$ to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in $G$ and give explicit formulae which describe both actions on the total cohomology $H^{*} (ℳ_{G}, 𝒞)$ in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group $S_{n}$ , the Weyl groups...

Cutting Hyperplane Arrangements.

J. Matousek (1991)

Discrete & computational geometry

Cutting Hyperplanes for Divide-and-Conquer.

B. Chazelle (1993)

Discrete & computational geometry

Displaying 1 – 11 of 11

Currently displaying 1 – 11 of 11