... is called the complete cd-index of [u, v], and it is denoted byψu,v(c, d). Noticethat the complete cd-index of [u, v] is an encoding of the distribution of the descent sets of each path ... 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 ... {2} (three of them), and {1, 2} (two of them).3 Complete cd-index 3.1 Complete cd-index of Bruhat intervalsBillera and Brenti [1] provided a way to encode the descents sets of paths in B(u, v)...