| author: | D. Merlini, R. Sprugnoli and M. C. Verri |
|---|---|
| title: | Human and constructive proof of combinatorial identities: an example from Romik |
| keywords: | Combinatorial identities, method of coefficients, Lagrange inversion, Riordan Arrays, WZ-method |
| abstract: | It has become customary to prove binomial identities by means of the method for automated proofs as developed by Petkovšek, Wilf and Zeilberger [PWZ96]. 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 [Rom03], 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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| reference: | D. Merlini and R. Sprugnoli and M. C. Verri (2005), Human and constructive proof of combinatorial identities: an example from Romik, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 383-392 |
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