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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Human and constructive proof of combinatorial identities: an example from Romik

Abstract

It has become customary to prove binomial identities by means of the method for automated proofs as developed by Petkovšek, Wilf and Zeilberger. In this paper, we wish to emphasize the role of "human'' and constructive proofs in contrast with the somewhat lazy attitude of relaying on "automated'' proofs. As a meaningful example, we consider the four formulas by Romik, related to Motzkin and central trinomial numbers. We show that a proof of these identities can be obtained by using the method of coefficients, a human method only requiring hand computations.
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Dates and versions

hal-01184212 , version 1 (13-08-2015)

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D. Merlini, R. Sprugnoli, M. C. Verri. Human and constructive proof of combinatorial identities: an example from Romik. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.383-392, ⟨10.46298/dmtcs.3377⟩. ⟨hal-01184212⟩

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