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Organization:  Rutgers University New Brunswick

 

Review #2

Proposal Number:

 

0901226

Performing Organization:

 

Rutgers Univ New Brunswick

NSF Program:

 

Algebra,Number Theory,and Combinatorics

Principal Investigator:

 

Zeilberger, Doron

Proposal Title:

 

Rigorous Experimental Combinatorics

Rating:

 

Excellent



REVIEW:

What is the intellectual merit of the proposed activity?

The work of Zeilberger has been enormously influential in combinatorics. He has been a champion of using the computer to explore a variety of combinatorial problems and to develop algorithms that allows one to verify and prove various identities that arise in combinatorics. He has had a large number of spectacular successes including the first proof of the alternating sign matrix conjecture, the development of the WZ method to prove holonomic identities, and many contributions to the theory of $q$-series, permutation statistics, and lattice paths.
He continues to be extremely productive and he and his students attack a wide variety of problems. In the period of his last grant, 6 students received their Ph.D. degree under his direction and he lists over 30 papers that are the result of his research.

It should come as no surprise that the current proposal again emphasizes the extensive use of computer methods to solve a variety of combinatorial problems. Some of the more intriguing problem areas include a series of interesting problems on higher dimensional lattice paths, permutation statistics, the Ruzumov-Stroganov conjectures on fully packed loops and alternating sign matrices, and extensions of the WZ theory to prove formulas involving multi-sums and multi-integrals like the famous Selberg integral formula.


What are the broader impacts of the proposed activity?

Zeilberger is tireless advocate to undergraduate students, graduate students, and other researchers of using computer exploration to solve mathematical problems. Thus he efforts will certainly have a broad impact on the mathematical community.

Summary Statement

Based on his past performance, I have no doubt that many new and exciting combinatorial results will be found by applying the type of computer based methods described in this proposal. He is tireless advocate to undergraduate students, graduate students, and other researchers of using computer exploration to solve mathematical problems. Thus he efforts will certainly have a broad impact on the mathematical community. Thus I definitely think that Zeilberger should be supported by the NSF and I would definitely rate this proposal in the Excellent category.


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