On the number of permutation polynomials over a finite field
The authors give a formula for the number \(N_q(q-2)\) of permutation polynomials of degree \(q-2\) over \(\mathbb{F}_q\) in terms of the permanent of a matrix. From this, they derive that NEWLINE\[NEWLINE |N_q(q-2)-(1-\text{\(\tfrac{1}{q}\)})(q-1)!|\leq q^{\frac{q}{2}-1}\,. NEWLINE\]
scientific article; zbMATH DE number 6618758
scientific article