# A direct encoding of Stoimenows matchings as ascent sequences

@article{Claesson2009ADE, title={A direct encoding of Stoimenows matchings as ascent sequences}, author={Anders Claesson and Mark Dukes and Sergey Kitaev}, journal={Australas. J Comb.}, year={2009}, volume={49}, pages={47-60} }

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.

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