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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
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