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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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