Pairs of noncrossing free Dyck paths and noncrossing partitions |
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| Authors: | William Y.C. Chen Sabrina X.M. Pang |
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| Affiliation: | a Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China
b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA |
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| 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. |
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| Keywords: | Dyck path Free Dyck path Plane partition Noncrossing partition Vacillating tableau |
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