Symbolic Summation and Combinatorial Identities

The problem of finding closed-form expressions for various sums is among ancient and attractive mathematical problems. In the early nineties, symbolic summation received a dramatic boost with the creation of Wilf-Zeilberger's algorithm for definite hypergeometric summation. Since then various computer packages that implement the algorithms have been developed.

In the 2009 GVSU REU participants will:

• explore, conjecture and formulate formulas for summation expressions,
• develop and master fundamental and useful skills for identity proving: combinatorial (counting) methods and computerized proof techniques (the Wilf-Zeilberger Method), and
• apply various computer summation algorithms for discovering and proving challenging and interesting combinatorial-identities.

To have some ideas about the above topics we suggest the following references:

• Introduction to WZ in 10 minutes
• More on WZ
• A = B
• Some important references on enumerative combinatorics:
  • Enumerative Combinatorics, Volumes 1 and 2, by Richard P. Stanley Read the first chaper in Volume 1.
  • Introduction to Enumerative Combinatorics by Miklos Bona Read part I of the book.

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