How to Generate all Possible WZ-pairs Algorithmically?

Start Date: July 20, 2018
Event Start Time: 5:00 PM
Event End Time: 5:45 PM
Seminar Series: Experimental Math Seminar
Presenter(s): Shaoshi Chen - KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Event Location: Hill Center- Room 525 | Rutgers University
Event Additional Info: <p><strong>(Note room change) </strong></p>
Presentation Type: Stand Alone Presentation
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 ζ(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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