Vol. 61, No. 2, 1975

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Permutation polynomials over the rational numbers

Clifton Earle Corzatt

Vol. 61 (1975), No. 2, 361–382
Abstract

Nonlinear polynomials, over the rational numbers, which permute the integers 0,1,N are investigated. The function ν(N) represents the minimum degree of all such polynomials. It is shown that

[N--+-1] ≦ ν(N) ≦ N − 1 for all N ≧ 13.
4

It is also shown that ν(N) N 2 for N odd and N 7, that ν(N) N 3 for N = 2 mod 6, and that if 𝜖 > 0 then ν(N) ((N 1)2)(1 𝜖) for N sufficiently large.

Mathematical Subject Classification 2000
Primary: 12E05
Secondary: 10M05
Milestones
Received: 20 December 1974
Published: 1 December 1975
Authors
Clifton Earle Corzatt