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A Random Permutation Model Arising in Chemistry

Part of: Combinatorial probability Chemistry

Published online by Cambridge University Press:  14 July 2016

Mark Brown ,
Erol A. Peköz  and
Sheldon M. Ross
Mark Brown*
Affiliation:
The City College of New York
Erol A. Peköz*
Affiliation:
Boston University
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗Postal address: Department of Mathematics, The City College of New York, New York, NY 10031-9100, USA. Email address: cybergarf@aol.com
∗∗Postal address: Department of Operations and Technology Management, Boston University, 595 Commonwealth Avenue, Boston, MA 02215, USA. Email address: pekoz@bu.edu
∗∗∗Postal address: Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
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Abstract

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We study a model arising in chemistry where n elements numbered 1, 2, …, n are randomly permuted and if i is immediately to the left of i + 1 then they become stuck together to form a cluster. The resulting clusters are then numbered and considered as elements, and this process keeps repeating until only a single cluster is remaining. In this article we study properties of the distribution of the number of permutations required.

Keywords

Random permutationhat-check problem

MSC classification

Secondary: 60C05: Combinatorial probability 92E20: Classical flows, reactions, etc.
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1060 - 1070
Copyright
Copyright © Applied Probability Trust 2008 

Footnotes

Supported by the National Security Agency under grant H98230-06-01-0149.

References

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[5] Rao, M. B. and Kasala, S. (2008). A discrete probability problem in chemical bonding. Preprint, Universite de Technologie de Compiegne, France.Google Scholar
[6] Ross, S. M. and Peköz, E. (2007). A Second Course in Probability. ProbabilityBookstore.com, Boston, MA.Google Scholar