On finite Thurston-type orderings of braid groups

Abstract We prove that for any finite Thurston-type ordering < T on the braid group Bn , the restriction to the positive braid monoid (, < T ) is a well-ordered set of order type ω ω n–2 . The proof uses a combinatorial description of the ordering < T . Our combinatorial description is based on a new normal form for positive braids which we call the (-normal form. It can be seen as a generalization of Burckel's normal form and Dehornoy's Φ-normal form (alternating normal form).