A direct encoding of Stoimenow's matchings as ascent sequences

In connection with Vassiliev's knot invariants, Stoimenow (1998) introduced certain matchings, also called regular linearized chord diagrams. Bousquet-Melou et al. (2008) gave a bijection from those matchings to unlabeled (2+2)-free posets; they also showed how to encode the posets as so called ascent sequences. In this paper we present a direct encoding of Stoimenow's matchings as ascent sequences. In doing so we give the rules for recursively constructing and deconstructing such matchings.