Combinatorics, or combinatorial mathematics, is a difficult field to define. It cuts across many branches of mathematics yet a mathematician will clearly sense which problems are of a combinatorial nature. Perhaps the simplest definition is that it is concerned with configurations or arrangements of elements, usually finite in number, into sets. Three basic types of problem are posed. Firstly the existence of certain configurations; secondly, once their existence is proved, the classification or enumeration of the configurations meeting the requirements imposed; and thirdly the construction of algorithms for finding the configurations in question.
- There elegant and elementary introductions to combinatorics are Berge (1971), Polya, Tarjan and Woods (1983) and Ryser (1963). A more advanced text is Aigner (1979).Google Scholar
- Berge, C. 1971. Principles of combinatorics. New York: Academic.Google Scholar
- Ryser, H.J. 1963. Combinatorial mathematics, Mathematical Association of America. New York: Wiley.Google Scholar