Geodesic
A decomposition algorithm for noncrossing trees
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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Based on the classic bijective algorithm for trees due to Chen, we present a decomposition algorithm for noncrossing trees. This leads to a combinatorial interpretation of a formula on noncrossing trees of size $n$ with $k$ descents. We also derive the formula for noncrossing trees of size $n$ with $k$ descents and $i$ leaves, which is a refinement of the formula given by Flajolet and Noy. As an application of our algorithm, we answer a question proposed by Hough, which asks for a bijection between two classes of noncrossing trees with a given number of descents.
DOI : 10.37236/3353
Classification : 05C85, 05C05, 05C30, 05A15
Mots-clés : noncrossing tree, descent, bijection 
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     author = {Lun Lv and Sabrina X.M. Pang},
     title = {A decomposition algorithm for noncrossing trees},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {1},
     doi = {10.37236/3353},
     zbl = {1300.05302},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3353/}
}
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Lun Lv; Sabrina X.M. Pang. A decomposition algorithm for noncrossing trees. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3353

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