The Method of Coefficients

Authors: Merlini, Donatella; Sprugnoli, Renzo; Verri, Maria Cecilia

Source: American Mathematical Monthly, Volume 114, Number 1, January 2007 , pp. 40-57(18)

Publisher: Mathematical Association of America

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Abstract:

The paper gives an account of the "method of coefficients" due to G. P. Egorychev. The method is used, often without any explicit reference, in the practice of formal power series and generating functions, both in combinatorics and in the analysis of algorithms. Here we show how we can start with a restricted series of general rules and proceed to obtain many results in these fields. Special emphasis is given to the rules of convolution, composition, and inversion, and to the evaluation of combinatorial sums.

Document Type: Research article

Publication date: 2007-01-01

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American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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