Conjectures P1-P15 for Coxeter groups with complete graph

Complete Growth Series of Coxeter Groups with more than Three Generators

Logspace computations in Coxeter groups and graph groups

Computing normal forms in groups (or monoids) is computationally harder than solving the word problem (equality testing), in general. However, normal form computation has a much wider range of applications. It is therefore interesting to investigate the complexity of computing normal forms for important classes of groups. For Coxeter groups we show that the following algorithmic tasks can be so...

Logspace Computations in Graph Groups and Coxeter Groups

Computing normal forms in groups (or monoids) is in general harder than solving the word problem (equality testing). However, normal form computation has a much wider range of applications. It is therefore interesting to investigate the complexity of computing normal forms for important classes of groups. We show that shortlex normal forms in graph groups and in right-angled Coxeter groups can ...

Essays on Coxeter groups Coxeter elements in finite Coxeter groups

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

The Complete cd-Index of Dihedral and Universal Coxeter Groups

We present a description, including a characterization, of the complete cd-index of dihedral intervals. Furthermore, we describe a method to compute the complete cd-index of intervals in universal Coxeter groups. To obtain such descriptions, we consider Bruhat intervals for which Björner and Wachs’s CL-labeling can be extended to paths of different lengths in the Bruhat graph. While such an ext...