Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Details Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

2008-04-18

arxiv.org/abs/0804.2930v2

Mathematics

Combinatorics

9 pages, 5 figures, revised version, to appear in Discrete Mathematics

Scientific paper

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.

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