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Number of mappings

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August 29, 2010
floor functioncombinatorics unsolvedcombinatorics

Problem Statement

Let SS be a kk-element set.
(a) Find the number of mappings f:Sā†’Sf : S \to S such that \text{(i) } f(x) \neq x \text{ for } x \in S,   \text{(ii) } f(f(x)) = x \text{ for }x \in S.
(b) The same with the condition (i)\text{(i)} left out.
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