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Omni-MATH / For a permutation σ of 1,2,…,7, a transposition is a swapping of two elements. Let f(σ) be the minimum number of transpositions necessary to turn σ into the permutation …

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problem

For a permutation σ\sigma of 1,2,…,71,2, \ldots, 7, a transposition is a swapping of two elements. Let f(σ)f(\sigma) be the minimum number of transpositions necessary to turn σ\sigma into the permutation 1,2,3,4,5,6,71,2,3,4,5,6,7. Find the sum of f(σ)f(\sigma) over all permutations σ\sigma of 1,2,…,71,2, \ldots, 7.
Plain-text mathematical notation (without MathML)
For a permutation σ of 1,2,…,7, a transposition is a swapping of two elements. Let f(σ) be the minimum number of transpositions necessary to turn σ into the permutation 1,2,3,4,5,6,7. Find the sum of f(σ) over all permutations σ of 1,2,…,7.
Original LaTeX notation
For a permutation $\sigma$ of $1,2, \ldots, 7$, a transposition is a swapping of two elements. Let $f(\sigma)$ be the minimum number of transpositions necessary to turn $\sigma$ into the permutation $1,2,3,4,5,6,7$. Find the sum of $f(\sigma)$ over all permutations $\sigma$ of $1,2, \ldots, 7$.

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task_id
f4997c15-7b7a-5869-9579-922ca7ed6370
task_key
test--f4997c15-7b7a-5869-9579-922ca7ed6370
task_revision_id
1
config / split
/ test

Official source

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