On the exact distributions of Eulerian and Simon Newcomb numbers associated with random permutations

James C. Fu, W. Y. Wendy Lou and Yueh-Jir Wang

Statistics & Probability Letters, 1999, vol. 42, issue 2, 115-125

Abstract: Eulerian and Simon Newcomb numbers are two of the most celebrated numbers associated with random permutations. Their distributions have been successfully used in various areas of statistics and applied probability. Conventionally, these distributions have been studied via combinatorial analysis. In this article, we provide a new, simple and unified probabilistic method based on the finite Markov chain imbedding technique to study the exact distributions of Eulerian and Simon Newcomb numbers. A new recursive equation which characterizes the Simon Newcomb numbers is obtained. We also show that many classical identities and recursive equations associated with Eulerian numbers are immediate consequences of our main result.

Keywords: Finite; Markov; chain; imbedding; Insertion; procedure; Transition; probability (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00176-X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:42:y:1999:i:2:p:115-125

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().