Matchings Avoiding Partial Patterns

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

Matchings Avoiding Partial Patterns

Authors

Chen, William Y. C.

Mansour, Toufik

Yan, Sherry H. F.

Description

We show that matchings avoiding certain partial patterns 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 Schröder paths without peaks at level one and matchings avoiding both patterns 12312 and 121323. Such objects are counted by the super-Catalan numbers or the little Schröder numbers. A refinement of the super-Catalan numbers is obtained by fixing the number of crossings in the matchings. In the sense of Wilf-equivalence, we find that the patterns 12132, 12123, 12321, 12231, 12213 are equivalent to 12312.
17 pages, 7 figures