Generalized Stirling permutations, families of increasing trees and urn models

Authors:
Svante Janson;Markus Kuba;Alois Panholzer
Affiliations:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden;Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria;Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 13
Cited 3

Average-case analysis of algorithms and data structures

Handbook of theoretical computer science (vol. A)
The r-multipermutations

Journal of Combinatorial Theory Series A
Inverse descents of r-multipermutations

Discrete Mathematics
P-partitions and q-Stirling numbers

Journal of Combinatorial Theory Series A
Poisson approximations for functionals of random trees

Proceedings of the seventh international conference on Random structures and algorithms
Hilbert Polynomials in Combinatorics

Journal of Algebraic Combinatorics: An International Journal
Varieties of Increasing Trees

CAAP '92 Proceedings of the 17th Colloquium on Trees in Algebra and Programming
Asymptotic degree distribution in random recursive trees

Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
On the degree distribution of the nodes in increasing trees

Journal of Combinatorial Theory Series A
Level of nodes in increasing trees revisited

Random Structures & Algorithms
Analytic Combinatorics

Analytic Combinatorics
Real Zeros and Normal Distribution for Statistics on Stirling Permutations Defined by Gessel and Stanley

SIAM Journal on Discrete Mathematics
Brownian bridge asymptotics for random mappings

Random Structures & Algorithms

Stable multivariate Eulerian polynomials and generalized Stirling permutations

European Journal of Combinatorics
Analysis of statistics for generalized stirling permutations

Combinatorics, Probability and Computing
Jacobi-Stirling polynomials and P-partitions

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bona (2007) [6] studied the distribution of ascents, plateaux and descents in the class of Stirling permutations, introduced by Gessel and Stanley (1978) [13]. Recently, Janson (2008) [17] 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 (2007) [6] and Janson (2008) [17], 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.