On the number of permutation polynomials over a finite field (Q2816453)
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scientific article; zbMATH DE number 6618758
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of permutation polynomials over a finite field |
scientific article; zbMATH DE number 6618758 |
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On the number of permutation polynomials over a finite field (English)
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22 August 2016
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permutation polynomial
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finite field
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permanent
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0.98053443
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0.9768957
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0.9682931
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0.96707714
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0.96641916
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0.9620963
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0.9587914
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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\]
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