Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.2

Bijections from Weighted Dyck Paths to Schröder Paths

Dan Drake
Department of Mathematical Sciences
Korea Advanced Institute of Science and Technology
Daejeon 305-701


Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schröder paths, is the same as the weight of Dyck paths in which downsteps from even height have weight 2. This work presents bijections from those Dyck paths to little Schröder paths, and from a similar set of Dyck paths to big Schröder paths. We show the effect of these bijections on the corresponding matchings, find generating functions for two new classes of lattice paths, and demonstrate a relationship with $231$-avoiding permutations.

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(Concerned with sequences A000108 A001003 A001263 A001850 A004148 A006318 A060693 A116363 A126216.)

Received June 15 2010; revised version received September 17 2010. Published in Journal of Integer Sequences, December 5 2010.

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