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Two statistics linking Dyck paths and non-crossing partitions. (English) Zbl 1217.05033
Summary: 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.

##### MSC:
 05A15 Exact enumeration problems, generating functions 05A18 Partitions of sets
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