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Chapter 3: Generating Functions introduces a central concept in the average-case analysis of algorithms: generating functions - a necessary and natural link between the algorithms that are our objects of study and analytic methods that are necessary to discover their properties. | ANALYTIC COMBINATORICS PART ONE http aofa.cs.princeton.edu 3. Generating Functions ANALYTIC COMBINATORICS PART ONE http aofa.cs.princeton.edu 3. Generating Functions OGFs Solving recurrences Catalan numbers EGFs Counting with GFs 3a.GFs.OGFs Ordinary generating functions Definition. z akzk is the ordinary generating function OGF k 0 of the sequence a0 a a2 . ak . Notation. zN is the coefficient of zN in A z sequence OGF 1 1 1 1 1 . EzN 1 z N 0 1 1 2 1 6 1 24 . y ez N N 0 zN ez 1 N Significance. Can represent an entire sequence with a single function.
