A Bound on Local Minima of Arrangements that Implies the Upper Bound Theorem.
A note on the Lawrence-Krammer-Bigelow representation.
A survey on local cohomology and 𝓓-modules
A tight lower bound for convexly independent subsets of the Minkowski sums of planar point sets.
An elementary chromatic reduction for gain graphs and special hyperplane arrangements.
An Invariant Property of Balls in Arrangements of Hyperplanes.
Arrangement of hyperplanes. I. Rational functions and Jeffrey-Kirwan residue
Arrangements and Milnor fibres.
Arrangements d'hyperplans et sommes de Gauss
Arrangements of arcs and pseudocircles.
Arrangements of hyperplanes and Lie algebra homology.
Arrangements of Oriented Hyperplanes.
Bergman complexes, Coxeter arrangements, and graph associahedra.
Cambrian fans
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...
Castles in the Air Revisited.
Cochain operations and subspace arrangements.
Colored partitions and a generalization of the braid arrangement.
Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.
Combinatorial Models for the Finite-Dimensional Grassmannians.
Combinatorial topology and the global dimension of algebras arising in combinatorics
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...