Stoimenow matchings avoiding multiple Catalan patterns simultaneously

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Lv, Shuzhen and Kitaev, Sergey (2026) Stoimenow matchings avoiding multiple Catalan patterns simultaneously. Discrete Mathematics, 349 (9). 115101. ISSN 0012-365X (https://doi.org/10.1016/j.disc.2026.115101)

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Abstract

Motivated by Vassiliev's knot invariants, Stoimenow introduced a special class of matchings, now known as Stoimenow matchings. These matchings have since been linked to various combinatorial structures enumerated by the Fishburn numbers. In a recent paper, a problem posed by Bevan et al. was addressed concerning the identification of subsets of Stoimenow matchings counted by the Catalan numbers. Five such subsets were presented, each defined by the avoidance of a single pattern, referred to as a Catalan pattern, within Stoimenow matchings. In the present paper, we extend this line of research by enumerating all cases of simultaneous avoidance of sets of Catalan patterns in Stoimenow matchings. This comprehensive analysis reveals connections to nine integer sequences listed in the OEIS.

ORCID iDs

Lv, Shuzhen and Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647;
CORE (COnnecting REpositories)