2008/04/18 by Chen, William Y. C., Pang, Sabrina X. M., Qu, Ellen X. Y. +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0804.2930
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.