Re: Divisibility property of binomial coefficients (Hoggatt triangles)

From: Michael J Hardy (mjhardy_at_mit.edu)
Date: 08/22/04 

Date: 21 Aug 2004 21:15:01 -0400

tchow@lsa.umich.edu wrote:

> Is it true, and if so how does one prove, that
>
> (n choose m) * (n choose m+1) * ... * (n choose m+k)
>
> is divisible by
>
> (n choose 0) * (n choose 1) * ... * (n choose k) ?

Hi. I vaguely recall seeing this as an exercise in Richard
Stanley's book. Not sure, though. But he would know, I
presume. (I emailed these comments to <tchow@lsa.umich.edu>
and the email bounced.) -- Mike