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Published in:
Gibbs Base Random Partitions Read chapter Read first chapter

2020 | OriginalPaper | Chapter

4. Distribution of Number of Levels in an \([\varvec{s}]\)-Specified Random Permutation

Author : James C. Fu

Published in: Pioneering Works on Distribution Theory

Publisher: Springer Singapore

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Abstract

Successions, Eulerian and Simon Newcomb numbers, and levels are the best-known patterns associated with \([\varvec{s}]\)-specified random permutations. The distribution of the number of rises was first studied in 1755 by Euler. However, the distribution of the number of levels in an \([\varvec{s}]\)-specified random permutation remained unknown. In this study, our main goal is to identify the distribution of the number of levels, which we achieve using the finite Markov chain imbedding technique and insertion procedure. An example is given to illustrate the theoretical result.

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previous chapter Error Bounds for the Normal Approximation to the Length of a Ewens Partition
next chapter Properties of General Systems of Orthogonal Polynomials with a Symmetric Matrix Argument
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Metadata
Title
Distribution of Number of Levels in an -Specified Random Permutation
Author
James C. Fu
Copyright Year
2020
Publisher
Springer Singapore
Book
Pioneering Works on Distribution Theory

Print ISBN: 978-981-15-9662-9

Electronic ISBN: 978-981-15-9663-6

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-15-9663-6_4

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