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Matchings Avoiding Partial Patterns | | William Y. C. Chen
; Toufik Mansour
; Sherry H. F. Yan
; | | Date: |
17 Apr 2005 | | Subject: | Combinatorics MSC-class: 05A05, 05C30 | math.CO | | Abstract: | 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. | | Source: | arXiv, math.CO/0504342 | | Services: | Forum | Review | PDF | Favorites | |
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