Permutation polynomials over the rational numbers

Clifton Earle Corzatt

Vol. 61 (1975), No. 2, 361–382

DOI: 10.2140/pjm.1975.61.361

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

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