# Local Maximas of various Permutations!

A permutation $$\pi$$ of $$\{1,2,\ldots,n\}$$ (with $$n \geq 3$$) has a local maximum at a position $$k$$ if the two neighbouring numbers (or, in case $$k=1$$ or $$k=n$$, the one neighbouring number) are both smaller than the number in position $$k$$.

• For Example : If $$n=5$$, then the permutation $$\{2,1,4,5,3 \}$$ has local maxima(s) in position(s) 1 and 4 (the numbers 2 and 5 respectively).

What is the average number of local maxima of a permutation of $$\{1,2,\ldots, n\}$$, averaging over all such permutations for $$n=2015$$ ?

Bonus - Generalize the above problem for $$n$$.

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