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Omni-MATH / Given a permutation σ of {1,2,…,2013}, let f(σ) to be the number of fixed points of σ - that is, the number of k∈{1,2,…,2013} such that σ(k)=k. If S is the set of all possible perm…

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problem

Given a permutation σ\sigma of {1,2,…,2013}\{1,2, \ldots, 2013\}, let f(σ)f(\sigma) to be the number of fixed points of σ\sigma - that is, the number of k∈{1,2,…,2013}k \in\{1,2, \ldots, 2013\} such that σ(k)=k\sigma(k)=k. If SS is the set of all possible permutations σ\sigma, compute ∑σ∈Sf(σ)4\sum_{\sigma \in S} f(\sigma)^{4} (Here, a permutation σ\sigma is a bijective mapping from {1,2,…,2013}\{1,2, \ldots, 2013\} to {1,2,…,2013}\{1,2, \ldots, 2013\}.)
Plain-text mathematical notation (without MathML)
Given a permutation σ of {1,2,…,2013}, let f(σ) to be the number of fixed points of σ - that is, the number of k∈{1,2,…,2013} such that σ(k)=k. If S is the set of all possible permutations σ, compute ∑_(σ∈S)f(σ)⁴ (Here, a permutation σ is a bijective mapping from {1,2,…,2013} to {1,2,…,2013}.)
Original LaTeX notation
Given a permutation $\sigma$ of $\{1,2, \ldots, 2013\}$, let $f(\sigma)$ to be the number of fixed points of $\sigma$ - that is, the number of $k \in\{1,2, \ldots, 2013\}$ such that $\sigma(k)=k$. If $S$ is the set of all possible permutations $\sigma$, compute $$\sum_{\sigma \in S} f(\sigma)^{4}$$ (Here, a permutation $\sigma$ is a bijective mapping from $\{1,2, \ldots, 2013\}$ to $\{1,2, \ldots, 2013\}$.)

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task_id
4a80dc74-9210-5533-b972-df2458ba3da7
task_key
test--4a80dc74-9210-5533-b972-df2458ba3da7
task_revision_id
1
config / split
/ test

Official source

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