Matchings avoiding partial patterns

William Y.C. Chen, Toufik Mansour, Sherry H.F. Yan

Research output: Contribution to journalArticlepeer-review


We show that matchings avoiding a certain partial pattern are counted by the 3-Catalan numbers. We give a characterization of 12312-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns 12312 and 121323 and Schröder paths without peaks at level one, which are counted by the super-Catalan numbers or the little Schröder numbers. A refinement of the super-Catalan numbers is derived by fixing the number of crossings in the matchings. In the sense of Wilf-equivalence, we use the method of generating trees to show that the patterns 12132, 12123, 12321, 12231, 12213 are all equivalent to the pattern 12312.

Original languageEnglish
Pages (from-to)1P
JournalElectronic Journal of Combinatorics
Issue number1 R
StatePublished - 18 Dec 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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