Abstract
As we all know, n elements can be ordered in n! ways. By selecting one of these orderings at random we obtain a random permutation. Such permutations are studied intensely nowadays using tools from combinatorics, probability and mathematics; there are also classical problems in this area. The present chapter gives some examples of what has been achieved, and shows the relationship to some other parts of mathematics. For example, we study the number of cycles in a random permutation and demonstrate their close relationships to Stirling numbers of the first kind. The last two sections, which are somewhat more advanced, show that sequences of continuous rv’s give rise to problems concerning random permutations as well.
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© 1994 Springer-Verlag New York, Inc.
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Blom, G., Holst, L., Sandell, D. (1994). Random permutations. In: Problems and Snapshots from the World of Probability. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4304-5_6
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DOI: https://doi.org/10.1007/978-1-4612-4304-5_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94161-5
Online ISBN: 978-1-4612-4304-5
eBook Packages: Springer Book Archive