Tag Archives: power series

Power Series and Generating Functions (III) – Partitions

Posted on March 19, 2012 by limsup

One particularly fruitful application of generating functions is in partition numbers. Let n be a positive integer. A partition of n is an expression of n as a sum of positive integers, where two expressions are identical if they can be obtained from each … Continue reading →

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Power Series and Generating Functions (II): Formal Power Series

Posted on February 19, 2012 by limsup

For today’s post, we shall first talk about the Catalan numbers. The question we seek to answer is the following. Let n be a positive integer. Given a non-associative operation *, find the number of ways to bracket the expression … Continue reading →

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Power Series and Generating Functions (I): Basics

Posted on February 5, 2012 by limsup

[ Background required: basic combinatorics, including combinations and permutations. Thus, you should know the formulae and and what they mean. Also, some examples / problems may require calculus. ] Note: this post is still highly relevant to competition-mathematics. 🙂 To … Continue reading →

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