The Complete <strong>cd</strong>-Index of Dihedral and Universal Coxeter Groups

Abstract

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 extension cannot be defined for all Bruhat intervals, it can be in dihedral and universal Coxeter systems.