MathDB

Let

\sigma_n

be a permutation of

\{1,\ldots,n\}

; that is,

\sigma_n(i)

is a bijective function from

\{1,\ldots,n\}

to itself. Define

f(\sigma)

to be the number of times we need to apply

\sigma

to the identity in order to get the identity back. For example,

f

of the identity is just

1

, and all other permutations have

f(\sigma)>1

. What is the smallest

n

such that there exists a

\sigma_n

with

f(\sigma_n)=k

Problem Statement