[seqfan] Re: OT: telling one-to-one polynomial maps in a finite field
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:
> Easy to use, low noise, lots of smart people, but a more general math
> knowledge source than seqfan.
> Seqfan Mailing list - http://list.seqfan.eu/
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