Generalized Stirling permutations, families of increasing trees and urn models

Details Generalized Stirling permutations, families of increasing trees and urn models Generalized Stirling permutations, families of increasing trees and urn models

2008-05-27

arxiv.org/abs/0805.4084v1

Mathematics

Combinatorics

25 pages, 3 figures, Keywords: Increasing trees, plane recursive trees, Stirling permutations, ascents, descents, urn models,

Scientific paper

Bona [2007+] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley [1978]. Recently, Janson [2008+] showed the connection between Stirling permutations and plane recursive trees and proved a joint normal law for the parameters considered by Bona. Here we will consider generalized Stirling permutations extending the earlier results of Bona and Janson, and relate them with certain families of generalized plane recursive trees, and also $(k+1)$-ary increasing trees. We also give two different bijections between certain families of increasing trees, which both give as a special case a bijection between ternary increasing trees and plane recursive trees. In order to describe the (asymptotic) behaviour of the parameters of interests, we study three (generalized) Polya urn models using various methods.

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