I know the functions should be Bijections, the number of bijections are m!= 120, (m = nuber of elements in domain ),But how to proceed for finding the number of functions such that f(f(n))=n ?
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writing mathematics at this site see, e.g., here, here, here and here. – Another User Jul 02 '22 at 18:30
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2Each element $(a)$ that is not mapped to itself, must be paired with an element $(b)$ such that $f(a) = b$ and $f(b) = a.$ Any satisfying function will either have $(0), (1),$ or $(2)$ such pairs. Enumerate by cases. – user2661923 Jul 02 '22 at 18:31
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This may be related to your question. See this Wikipedia page as well. – Zeekless Jul 02 '22 at 18:32
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3Quite a few methods are covered by the answers to the question Number of functions $f : A \to A$ with $f(f(x)) = x$. If you have questions regarding any of their approaches, please edit your question to reflect the same. – Sarvesh Ravichandran Iyer Jul 03 '22 at 04:50