Gridpoint Method for Proving Combinatorial Identities
Gridpoint Method for Proving Combinatorial Identities

Summary/Abstract: Proofs are an important part of mathematical understanding. The three basic methods of proving combinatorial identities are mathematical induction, algebraic calculation, and combinatorial proofs. The last two of them are usually based on socalled double counting, which means counting the number of elements in one group with two different methods. In this article, we show an approach that uses gridpoints (points with integer coordinates) to calculate the number of elements of a set expressed by the left and the right side of a combinatorial identity. The gridpoint method for combinatorial calculation is known from [1] and [2]. This article presents the advantages of gridpoint approach in two aspects. The first one is simplifying the proofs in some cases, and the second one, to show students a way for independent work in invention (or reinvention) of combinatorial identities using the gridpoint method combining integer coordinates in an appropriate way. Finally, we discuss the acceptance of proofs by the gridpoint method as explanatory proofs.

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