Algorithmic proofs of combinatorial identities

Abstract

Mathematical identities may be proved by direct calculation, mathematical induction, bijections and so on. Sometimes algorithmic approach to prove identities can be very useful. For example, this approach may provide new identities and closed formulas of sums. However, since there is no global algorithm which can be applied to all kinds of identities and terms, we will focus on identities and terms which tend to occur in combinatorics : hypergeometric identities and terms. In this thesis, we construct and prove such algorithms. This thesis is totally based on the book [8].