Lehmer code: Difference between revisions

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\end{matrix}
</math>
where the final line is the Lehmer code (at each line theone boldfacesubtracts entry is subtracted1 from the larger entries to itsthe right of itthe boldface element to form the next line).
 
For decoding a Lehmer code into a permutation of a given set, the latter procedure may be reversed: for each entry ''x'', in order from right to left, correct the items to its right by adding 1 to all those (currently) greater than or equal to ''x''; finally interpret the resulting permutation of {0, 1, … {{math|''n'' − 1}}} as sequence numbers (which amounts to adding 1 to each entry if a permutation of {1, 2, … ''n''} is sought). Alternatively the entries of the Lehmer code can be processed from left to right, and interpreted as a number determining the next choice of an element as indicated above; this requires maintaining a list of available elements, from which each chosen element is removed. In the example this would mean choosing element 1 from {A,B,C,D,E,F,G} (which is B) then element 4 from {A,C,D,E,F,G} (which is F), then element 0 from {A,C,D,E,G} (giving A) and so on, reconstructing the sequence B,F,A,G,D,E,C.