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Bookmark or Share- Salié permutations and fair permutations - MathOverflowWrite a fair permutation in cycle form, as follows. First write all cycles of length $>1$ in decreasing order of their smallest element, with the smallest element of each cycle written as the leftmost element of the cycle.
- 321-avoiding and parity-alternating permutations - MathOverflowIt is classical that 321-avoiding permutations are enumerated by the Catalan numbers. A permutation is parity-alternating if it sends even integers to even integers, and odd integers to odd.
- nt.number theory - Salie-type sum bound - MathOverflowI am trying to find a bound for these Salie-type sums. When $\beta = 1$, the bound $|S(a,b,1)| \leq 2 \sqrt{p}$ is due to Salie. When $\beta \geq 2$ is even, the Jacobi symbol is identically $1$ and so the sum reduces to a Kloosterman sum
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