Re: [math-fun] Expansion of charpoly's in terms of traces ?

On Fri, Dec 4, 2009 at 9:11 AM, Eugene Salamin <gene_salamin@yahoo.com> wrote:

I seem to be misunderstanding something here.  The binomial coefficient x_C_k = x(x-1)...(x-k+1)/k! in char 0.  How is it defined in finite char?

You can define it by Pascal's triangle. I think that's exactly equivalent to defining it in terms of being a binomial coefficient. The formula you give is better viewed as a consequence of the definition rather than the definition itself, in my opinion. --Joshua Zucker