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Another interpretation of the number of derangements. (Une autre interprétation du nombre des dérangements.) (French) Zbl 0925.05009
Summary: Another class of permutations in a one-to-one correspondence with the derangements is introduced that provides a natural interpretation of the usual recurrence: $$d(n)=nd(n-1)+1$$ ($$n$$ even) and $$d(n)=nd(n-1)-1$$ ($$n$$ odd). Those permutations are exactly those whose Lehmer codings start with an even number of 1’s.

##### MSC:
 05A15 Exact enumeration problems, generating functions 05A05 Permutations, words, matrices
##### Keywords:
permutations; derangements; Lehmer codings
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