Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

William Y. C. Chen; Sabrina X. M. Pang; Ellen X. Y. Qu; Richard P. Stanley

Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Combinatorics 2008-07-27 v2

Authors: William Y. C. Chen , Sabrina X. M. Pang , Ellen X. Y. Qu , 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.

Keywords

noncrossing Dyck paths noncrossing partitions vacillating tableaux bijection Labelle merging algorithm combinatorics

Cite

@article{arxiv.0804.2930,
  title  = {Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions},
  author = {William Y. C. Chen and Sabrina X. M. Pang and Ellen X. Y. Qu and Richard P. Stanley},
  journal= {arXiv preprint arXiv:0804.2930},
  year   = {2008}
}

Comments

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

Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Abstract

Keywords

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