Major Index on Catalan Combinatorics
Abstract
We study the two statistics, the inversion number and the major index, on Catalan combinatorial objects such as r-Dyck paths, r-Stirling permutations, non-crossing partitions, Dyck tilings, and symmetric Dyck paths. We show that they are equidistributed with the inversion number or the major index on Dyck paths.
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