Pairs of noncrossing free Dyck paths and noncrossing partitions
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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.
9 pages, 5 figures, revised version, to appear in Discrete Mathematics
- Department of Mathematics Massachusetts Institue of Technolgy (MIT) United States
- Massachusetts Institute of Technology Dept. of Economics United States
- Massachusetts instute of technology EAPS United States
- Nankai University China (People's Republic of)
- Massachusetts Institute of Technology United States
plane partition, vacillating tableau, free Dyck path, noncrossing partition, Theoretical Computer Science, Noncrossing partition, Plane partition, Partitions of sets, Combinatorial aspects of representation theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), Free Dyck path, Vacillating tableau, Combinatorial identities, bijective combinatorics
plane partition, vacillating tableau, free Dyck path, noncrossing partition, Theoretical Computer Science, Noncrossing partition, Plane partition, Partitions of sets, Combinatorial aspects of representation theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), Free Dyck path, Vacillating tableau, Combinatorial identities, bijective combinatorics
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