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Experimental Mathematics Seminar

How to generate all possible WZ-pairs algorithmically? 

Shaoshi Chen, KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Location:  Hill 525 (Note room change) 
Date & time: Friday, 20 July 2018 at 5:00PM - 6:00PM

Abstract:  The Wilf-Zeilberger theory has become a bridge between symbolic computation and combinatorics. 

Through this bridge, not only classical combinatorial identities from handbooks and long-standing conjectures in enumerative combinatorics are proved algorithmically, but also some new identities and conjectures related to mathematical constants are discovered via computerized guessing. 
WZ-pairs play a leading role in the WZ theory whose early applications can be traced back to Andrei Markov's 1890 method for convergence-acceleration of series for computing ?(3). For applications, it is crucial to have WZ-pairs at hand. In the previous works, WZ-pairs are cooked either by guessing from the identities to be proved using Gosper'algorithm or by certain transformations from a given WZ-pair. 
In this talk, we first present a structure theorem on the possible form of all rational WZ-pairs, and then we will illustrate how one could go beyond the rational case using Ore-Sato theorem. 
We hope these studies could enable us discover more combinatorial identities in an intrinsic and algorithmic way. 

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