[seqfan] Re: OT: telling one-to-one polynomial maps in a finite field

Roland Bacher Roland.Bacher at ujf-grenoble.fr
Mon May 17 16:13:15 CEST 2010

Inspired by this question, I posted a question at MO (Math-Overflow)
asking for possible degrees of such polynomials.

I guess that the group of such polynomials (modulo reduction by 
$x^q-x$) is generated by affine bijections and by maps of the form 
x-> x^k with k coprime to q-1. This gives no answer to your question
because it is probably difficult to write a given polynomial (up to x^q-x,
of course) explicitely as a product of such generators.


On Mon, May 17, 2010 at 09:28:02AM -0400, Mitch Harris wrote:
> > Sorry for Off-Topic, my pain is:
> > 
> > Is it possible to *efficiently* (probabilistically) tell if a 
> > polynomial map K^n -> K^n is one-to-one where K is a *finite field* ?
> The best current place to try to get such questions answered:
>   http://mathoverflow.net/
> Easy to use, low noise, lots of smart people, but a more general math
> knowledge source than seqfan.
> Mitch
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> Seqfan Mailing list - http://list.seqfan.eu/

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