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Combinatorics by Peter J. Cameron

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15.  Enumeration under group action

‘I count a lot of things that there’s no need to count,’ Cameron said. ‘Just because that’s the way I am. But I count all the things that need to be counted.’

Richard Brautigan, The Hawkline Monster (1974)

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TOPICS: Orbit-counting Lemma; cycle index; enumeration of functions by weight

TECHNIQUES: Calculation of cycle index

ALGORITHMS:

CROSS-REFERENCES: Direct and wreath products (Chapter 14); Stirling numbers (Chapter 5); unlabelled structures (Chapters 2, 14); symmetric polynomials (Chapter 13)

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In this chapter, ...

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