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On the sum $\sum_{\pi\in S_{n}}e^{2\pi i\sum_{k=1}^{n}k\pi(k)/n}$
Motivated by Question 316142 of mine, I consider the new sum
$$S(n):=\sum_{\pi\in S_{n}}e^{2\pi i\sum_{k=1}^{n}k\pi(k)/n}$$
for any positive integer $n$, where $S_n$ is the symmetric group of all the ...
1
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Some $p$-adic congruences involving permutations
Motivated by my study of determinants and permanents, here I present several conjectures on $p$-adic congruences involving permutations.
As usual, we let $S_n$ be the symmetric group consisting of all ...