Analysis of Statistics for Generalized Stirling Permutations

Content Provider	Scilit
Author	Kuba, Markus Panholzer, Alois
Copyright Year	2011
Description	In this work we give a study of generalizations of Stirling permutations, a restricted class of permutations of multisets introduced by Gessel and Stanley [15]. First we give several bijections between such generalized Stirling permutations and various families of increasing trees extending the known correspondences of [20, 21]. Then we consider several permutation statistics of interest for generalized Stirling permutations as the number of left-to-right minima, the number of left-to-right maxima, the number of blocks of specified sizes, the distance between occurrences of elements, and the number of inversions. For all these quantities we give a distributional study, where the established connections to increasing trees turn out to be very useful. To obtain the exact and limiting distribution results we use several techniques ranging from generating functions, connections to urn models, martingales and Stein's method.
Related Links	http://www.dmg.tuwien.ac.at/kuba/preprintStirblock.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/488A8224069AE788ADDD620CE809EC55/S0963548311000381a.pdf/div-class-title-analysis-of-statistics-for-generalized-stirling-permutations-div.pdf
Ending Page	910
Page Count	36
Starting Page	875
ISSN	09635483
e-ISSN	14692163
DOI	10.1017/s0963548311000381
Journal	Combinatorics, Probability and Computing
Issue Number	6
Volume Number	20
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2011-11-01
Access Restriction	Open
Subject Keyword	Combinatorics, Probability and Computing Artificial Intelligence Generalized Stirling Permutations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics