Finite Thurston Type Orderings on Dual Braid Monoids

We give a combinatorial description of a finite Thurston type ordering < on the dual braid monoid B n by introducing the C-normal form and prove that the order-type of the well-ordered set (B n , <) is ωω n−2 . The C-normal form can be seen as a generalization of the rotating normal form defined by Fromentin and it is also a natural extension of C-normal form of the positive braid monoids defined by the author.