Lehmer code: Difference between revisions

Revision as of 23:53, 25 January 2014

Revision as of 10:05, 14 December 2014

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==Applications to combinatorics and probabilities==

=== Independence of relative ranks ===

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{{Main|Secretary problem}}

This is an optimal stop problem, a classic in decision theory, statistics and applied probabilities, where a random permutation is gradually revealed through the first elements of its Lehmer code, and where the goal is to stop exactly at the element k such as σ(k)=n, whereas the only available information (the k first values of the Lehmer code) is not sufficient to compute σ(k).

In less mathematical words : a series of n applicants are interviewed one after the other. The interviewer must hire the best applicant, but must make his decision (“Hire” or “Not hire”) on the spot, without interviewing the next applicant (and ''a fortiori'' without interviewing all applicants).

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==See also==

{{Portal box|Statistics|Discrete mathematics|Computer science}}

*[[Bernoulli distribution]]