• Corpus ID: 16492464

# A direct encoding of Stoimenows matchings as ascent sequences

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}
}
• Published 8 October 2009
• Mathematics, Computer Science
• Australas. J Comb.
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.
14 Citations

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: This is an overview of the history of the combinatorics group that was born in Gothenburg, Sweden, in the late 1990s and then lived in Reykjav´ık, Iceland, and now in Glasgow, Scotland.

## References

SHOWING 1-2 OF 2 REFERENCES

We treat an enumeration problem of chord diagrams, which is shown to yield an upper bound for the dimension of the space of Vassiliev invariants for knots. We give an asymptotical estimate for this