D. Merlini ; R. Sprugnoli ; M. C. Verri - Human and constructive proof of combinatorial identities: an example from Romik

dmtcs:3377 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3377
Human and constructive proof of combinatorial identities: an example from Romik

Authors: D. Merlini 1; R. Sprugnoli 1; M. C. Verri 1

  • 1 Dipartimento di Sistemi e Informatica

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.


Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: WZ-method,Combinatorial identities,method of coefficients,Lagrange inversion,Riordan Arrays,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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