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p. 504. A combinatorial zoolocked

  • Robin Wilson

Abstract

‘A combinatorial zoo’ presents a menagerie of combinatorial topics, ranging from the box (or pigeonhole) principle, the inclusion–exclusion principle, the derangement problem, and the Tower of Hanoi problem that uses combinatorics to determine how soon the world will end to Fibonacci numbers, the marriage theorem, generators and enumerators, and counting chessboards, which involves symmetry. The method used to average the numbers of colourings that remain unchanged by each symmetry in this latter problem is often called ‘Burnside’s lemma’. This concept has since been developed into a much more powerful result, which has been used to count a wide range of objects with a degree of symmetry, such as graphs and chemical molecules.

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