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REVIEW:
What is the intellectual merit of the proposed activity?
The proposal is highly original and creative. It develops
techniques and machinery in computer algebra to attack several
important problems in combinatorics, ranging from combinatorial
identities, analysis, enumeration, probability, extremal proplems, and
graph theory. The results would greatly advance the knowledge in
science and technology.
The PI is one of the main founder of WZ-theory, and an world
expert in computer algebra. He is extremally fruitful in his previous
NSF grants, and made a great progress in his area. There is no doubt
that he would contribute substantially in the proposed research.
What are the broader impacts of the proposed activity?
The methodology of computer-generated research described have had
applications in many other parts of mathematics, and in broader areas
of engineering, science, and technology. The progress in the
proposed research has potential to enhance the infrastructure of research and education, even to our everyday life.
The PI's research projects have been well-participated by
under-represented groups, and had yield several promising young
researchers in various minority groups. In addition to publishing
research articles, the PI and his students developed several software
packages. Many of them can be downloaded from the internet.
Summary Statement
This is a high quality proposal on very creative and original
research topics. The PI has demonstraded his ability in leading such
a research activity, and has already made great contribution through
the past research. This is one of the best proposal, and definitely
should be funded.
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