Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-21T11:23:49.149Z Has data issue: false hasContentIssue false
  • English
  • Français

A Random Permutation Model Arising in Chemistry

Part of: Chemistry Combinatorial probability

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Arratia, R. and Tavaré, S. (1992). The cycle structure of random permutations. Ann. Prob. 20, 1567–1591.CrossRefGoogle Scholar
[2] De Montmort, P. R. (1708). Essay d'Analyse sur le Jeux de Hazard. Quillau, Paris.Google Scholar
[3] Diaconis, P., Fulman, J. and Guralnick, R. (2008). On fixed points of permutations. J. Algebraic Combin. 28, 189–218.CrossRefGoogle Scholar
[4] Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. I, 3rd edn. John Wiley, New York.Google Scholar
[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