Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions
William Y.C. Chen, Sabrina X.M. Pang, Ellen X.Y. Qu, and Richard P. Stanley
Abstract: Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n + 1] with n + 1 blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.
AMS Classification: 05A10, 05A15
Keywords: Dyck path, free Dyck path, plane partition, noncrossing partition, vacillating tableau