Combinatorics (Fall 2010)/Generating functions: Difference between revisions
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imported>WikiSysop Created page with '== Ordinary Generating Functions == == Exponential Generating Functions ==' |
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== | == Generating Functions == | ||
In Stanley's magnificent book ''Enumerative Combinatorics'', he called the generating function "the most useful but most difficult to understand method (for counting)". | |||
The solution to a counting problem is usually represented as some <math>a_n</math> depending a parameter <math>n</math>. Sometimes this <math>a_n</math> is called a ''counting function'' as it is a function of the parameter <math>n</math>, but we can also treat it just as a infinite series: | |||
:<math>a_0,a_1,a_2,\ldots</math> | |||
Revision as of 03:02, 13 July 2010
Generating Functions
In Stanley's magnificent book Enumerative Combinatorics, he called the generating function "the most useful but most difficult to understand method (for counting)".
The solution to a counting problem is usually represented as some [math]\displaystyle{ a_n }[/math] depending a parameter [math]\displaystyle{ n }[/math]. Sometimes this [math]\displaystyle{ a_n }[/math] is called a counting function as it is a function of the parameter [math]\displaystyle{ n }[/math], but we can also treat it just as a infinite series:
- [math]\displaystyle{ a_0,a_1,a_2,\ldots }[/math]