More general are "exceptional polynomials" which were the subject of Dickson's thesis. A polynomial over a finite field is exceptional if it induces a one-to-one mapping on infinitely many extensions of the finite field. The following recent paper talks about classes of exceptional polynomials in characteristic 2: http://annals.math.princeton.edu/wp-content/uploads/annals-v172-n2-p12-p.pdf Victor On Sun, Mar 20, 2016 at 12:43 AM, Henry Baker <hbaker1@pipeline.com> wrote:
So Dickson worked on this problem in 1896 ! I'll have to track down his work.
Thanks very much, Victor -- I thought there might be some literature on this problem, but I didn't know what to search for. I guessed correctly that other people also called them "permutation polynomials".
At 06:46 PM 3/19/2016, Victor Miller wrote:
My former colleague, Mike Zieve (now a professor at MIchigan) has written a number of papers about permutation polynomials, the latest is http://arxiv.org/pdf/1312.1325.pdf . It gives a lot of references to known results and to his previous work.
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