Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: A Case Study in Experimental (Yet Fully Rigorous!) Mathematics: The Asymptotic Independence of the Two Main Permutation Statistics
Speaker: Doron Zeilberger, Rutgers University
Date: Thursday, November 4, 2010 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
I will describe the computer-assisted proof, by my student Andrew Baxter and myself, of the intriguing fact that the two most important permutation statistics, namely the number of inversions and the major index are asymptotically independent (all the terms will be explained, the talk does not assume any previous knowledge of combinatorics or probability).
At the same time, I will debunk several common prejudices of many mathematicians: "computers can's prove, they can only compute", "you can't generalize from finitely many cases", and "a math article has to be boring in order to be correct". I will also suggest a more effective, and much more reliable, way for future scholarly communication, rather than the current "peer"-reviewed system, that uses anonymous referees.
For the mathematical part see:
this masterpiece.
For the meta-mathematical part see:
Opinion 3 of DZ
Opinion 97 of DZ
Opinion 112 of DZ