RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

sponsored by the

Rutgers University
Department of Mathematics

and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Founded 2003 by Drew Sills and Doron Zeilberger.

Former co-organizers: Drew Sills (2003-2007), Moa ApaGodu (2005-2006), Lara Pudwell (2006-2008), Andrew Baxter (2008-2011), Brian Nakamura (2011-2013), Edinah Gnang (2011-2013), Matthew Russell (2013-2016), Nathan Fox (2016-2017), Bryan Ek (2017-2018)

Current co-organizers:
Doron Zeilberger (doronzeil {at} gmail [dot] com)
Mingjia Yang (my237 {at} math [dot] rutgers [dot] edu)

Archive of Previous Speakers and Talks You can find links to videos of some of these talks as well. Currently, our videos are being posted to our Vimeo page. Previously, we had videos posted on our YouTube page.


If you would like to be added to the weekly mailing list, email Mingjia Yang (my237@math...).

Forthcoming Talks

Unless otherwise specified, seminars will be held in Hill 705 on the date indicated from 5:00 PM to 5:48 PM. Professor Zeilberger has promised to enforce the time limits.




Special Summer 2018 Talk(s)

Date: Friday, July 20th, 2018
Time: 4:00pm
Speakers: Elaine Wong and Christoph Koutschan, (joint talk), Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences
Title: Symbolic evaluation of determinants and rhombus tilings of holey hexagons
Abstract:
          We investigate a curious determinant that was first mentioned by George Andrews in 1980 in the context of descending plane partitions. It is found to be a special instance of a two-parameter family of determinants that count certain collections of nonintersecting lattice paths, or, equivalently, cyclically symmetric rhombus tilings of a hexagon with several triangular holes inside. We find closed forms for several one-parameter subfamilies, both by applying combinatorial arguments and by applying Zeilberger's "holonomic ansatz".


Date: Friday, July 20th, 2018
Time: 5:00pm
Speaker: Shaoshi Chen, KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Title: How to generate all possible WZ-pairs algorithmically?
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.





This page is maintained by Mingjia Yang. Send comments to my237 {at} math [dot] rutgers [dot] edu.