Geodesic
Two statistics linking Dyck paths and non-crossing partitions
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We introduce a pair of statistics, maj and sh, on Dyck paths and show that they are equidistributed. Then we prove that this maj is equivalent to the statistics $ls$ and $rb$ on non-crossing partitions. Based on non-crossing partitions, we give the most obvious $q$-analogue of the Narayana numbers and the Catalan numbers.
DOI : 10.37236/570
Classification : 05A15, 05A18 
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     author = {Haijian Zhao and Zheyuan Zhong},
     title = {Two statistics linking {Dyck} paths and non-crossing partitions},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/570},
     zbl = {1217.05033},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/570/}
}
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Haijian Zhao; Zheyuan Zhong. Two statistics linking Dyck paths and non-crossing partitions. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/570

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