We introduce analogues of the lattice of non-crossing set partitions for the classical reflection
groups of types B and D. The type B analogues (first considered by Montenegro in a different …

We situate the noncrossing partitions associated with a finite Coxeter group within the
context of the representation theory of quivers. We describe Reading's bijection between …

This work is based on my habilitation thesis which I prepared at Berlin's Humboldt-University
while I was an assistant professor at the computer science department in the years 1994 …

This chapter treats error-correcting codes and their weight enumerator as the center of
several closely related topics such as arrangements of hyperplanes, graph theory, matroids …

In this paper, we study lattices that posess both the properties of being extremal (in the
sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call …

We survey three methods for proving that the characteristic polynomial of a finite ranked
lattice factors over the nonnegative integers and indicate how they have evolved recently …

Let A be a Coxeter hyperplane arrangement, that is the arrangement of reflecting
hyperplanes of an irreducible finite Coxeter group. A deformation of A is an affine …

We introduce a new method for showing that the roots of the characteristic polynomial of
certain finite lattices are all nonnegative integers. This method is based on the notion of a …

The Orlik–Solomon algebra A (G) of a matroid G is the free exterior algebra on the points,
modulo the ideal generated by the circuit boundaries. On one hand, this algebra is a …

It is known that a graded lattice of rank n is supersolvable if and only if it has an EL-labelling
where the labels along any maximal chain are exactly the numbers 1, 2,…, n without …