Some Problems in Combinatorics and Analysis That Can Be Explored Using Generating Functions

Alexander A. Roytvarf

A chapter in Thinking in Problems, 2013, pp 291-318 from Springer

Abstract: Abstract For a finite (or countably infinite) sequence an, the generating function (or series) is defined as the polynomial (resp. formal series) ∑antn . For a multisequence am,n,…, the generating function is a polynomial or series in several variables ∑a m,n,… t m u n Various problems of combinatorial analysis and probability theory are successfully explored with such powerful tools as generating functions. In this chapter readers will encounter several problems related to the combinatorics of binomial coefficients, theory of partitions, and renewal processes in probability theory that can be explored using generating functions. The problems of the first two groups does not require the ability to deal with power series (likewise, the problems of the second group assume no familiarity with the theory of partitions) and can be solved by readers with limited experience.

Keywords: Multisequence; Linear Recursion Relation; Linear Independence; Euler Series; Positive Integer Coefficients (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8406-8_11

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DOI: 10.1007/978-0-8176-8406-8_11

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