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We exploit a bijection between plane recursive trees and Stirlingpermutations; this yields the equivalence of some results previously provenseparately by different methods for the two types of objects as well as somenew results. We also prove results on the joint distribution of the numbers ofascents, descents and plateaux in a random Stirling permutation. The proof usesan interesting generalized Polya urn

Plane recursive trees, Stirling permutations and an urn model