  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.
