Abstract
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.
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References
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).
Aigner, M. 1979. Combinatorial theory. Berlin: Springer.
Berge, C. 1971. Principles of combinatorics. New York: Academic.
Polya, G., R.E. Tarjan, and D.R. Woods. 1983. Notes on introductory combinatorics. Boston: Birkhauser.
Ryser, H.J. 1963. Combinatorial mathematics, Mathematical Association of America. New York: Wiley.
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Kirman, A.P. (2018). Combinatorics. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_58
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DOI: https://doi.org/10.1057/978-1-349-95189-5_58
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Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
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