binomial(5,2) Proofs that binomial(n,k) ≤ binomial(n,k+1) if k < n/2

By Doron Zeilberger

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Written: March 4, 2010.
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and .

This is an almost exact transcript of a colloquium talk that I gave at Columbia University on Feb. 17, 2010. The abstract warned that people who would be offended by a talk that they could actually understand should not come. It seems that there are lots of such people, as only nineteen people showed up. But I believe that those people who skipped the talk would be offended by any talk, whether or not they had any chance of understanding it, that is not exactly in their narrow specialty. The Tower of Babel has gotten out of hand.

Added March 10, 2010: read interesting comments by Francois Bergeron .
Added April 6, 2010: read Murali K. Srinivasan's elegant note .
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