From: Joshua Zucker <joshua.zucker@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Fri, December 4, 2009 9:21:46 AM Subject: 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 _______________________________________________ I must be stupid today; I still don't understand. I can write Pascal's triangle in F_q, but what is x_C_k? -- Gene