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fixed broken link to springerlink.com; added citation information in tooltip; "corrected" title of paper (it really does say "identy" instead of "identity")
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edit approved Jun 5, 2022 at 12:45
The Amplitwist
edit approved Jun 5, 2022 at 12:45
The Amplitwist
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The trace of a permutation matrix is the number of fixed points of the corresponding permutation. This is a special case of the identity proved in "An identity for fixed points of permutationsAn identy for fixed points of permutations" by Goldman, where the average of the $k^{th}$ powers of the number of fixed points is shown to be the $k^{th}$ Bell number $B_k$ when $k<n$. Your case follows because $B_2=2$.

The trace of a permutation matrix is the number of fixed points of the corresponding permutation. This is a special case of the identity proved in "An identity for fixed points of permutations" by Goldman, where the average of the $k^{th}$ powers of the number of fixed points is shown to be the $k^{th}$ Bell number $B_k$ when $k<n$. Your case follows because $B_2=2$.

The trace of a permutation matrix is the number of fixed points of the corresponding permutation. This is a special case of the identity proved in "An identy for fixed points of permutations" by Goldman, where the average of the $k^{th}$ powers of the number of fixed points is shown to be the $k^{th}$ Bell number $B_k$ when $k<n$. Your case follows because $B_2=2$.

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Jonas Meyer
Jonas Meyer
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The trace of a permutation matrix is the number of fixed points of the corresponding permutation. This is a special case of the identity proved in "An identity for fixed points of permutations" by Goldman, where the average of the $k^{th}$ powers of the number of fixed points is shown to be the $k^{th}$ Bell number $B_k$ when $k<n$. Your case follows because $B_2=2$.