Tag Archives: generating functions

Burnside’s Lemma and Polya Enumeration Theorem (2)

[ Acknowledgement: all the tedious algebraic expansions in this article were performed by wolframalpha. ] Counting Graphs One of the most surprising applications of Burnside’s lemma and Polya enumeration theorem is in counting the number of graphs up to isomorphism. … Continue reading

Random Walk and Differential Equations (I)

Consider discrete points on the real line, indexed by the integers … -3, -2, -1, 0, 1, 2, … . A drunken man starts at position 0 and time 0. At each time step, he may move to the left … Continue reading

Power Series and Generating Functions (IV) – Exponential Generating Functions

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Power Series and Generating Functions (III) – Partitions

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