Abstract
In 1937, George Pólya wrote what is considered one of the most significant papers in 20th-century mathematics. The article contained one theorem and 100 pages of applications. It introduced a combinatorial method which led to unexpected applications to diverse problems in science like the enumeration of isomers of chemical compounds. Pólya’s theory of enumeration was discussed in detail in [1] by Shriya Anand, a summer student of the author. In what follows, we briefly recall the theory and complement the earlier article by adding some other applications not discussed there.
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Suggested Reading
Shriya Anand, How to count — an exposition of Pólya’s theory of enumeration, Resonance, Vol.7, No.9, pp.19–35, 2002.
G Pólya and R C Read, Combinatorial enumeration of groups, graphs, and chemical compounds, Springer-Verlag, 1987.
David L Reiner, Enumeration in music theory, The American Mathematical Monthly, pp.51–54, January, 1985.
G Pólya, Kombinatorische Anzahlbestimmungen fur Gruppen, Graphen und chemische Verbindungen, Acta Mathematica, Vol.68, pp.145–254, 1937.
V Krishnamurthy, Combinatorics — Theory and Applications, Affiliated East-West Press Private Limited, 1985.
J H Redfield, The theory of group reduced distributions, Amer. J.Math., Vol.49, pp.433–455, 1927.
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B Sury has been with the ISI, Bangalore since 1999. Apart from his interest in teaching mathematics at the undergraduate level, he has also long-standing interest in the mathematical olympiad programme in the country.
He would like to introduce this article on Pólya by: Believe me, Mathematics is an asset in counting (it can aid and abet) of different isomers — even stereo. We’d have bid it cheerio but for this magic PET !
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Sury, B. Pólya’s one theorem with 100 pages of applications. Reson 19, 338–346 (2014). https://doi.org/10.1007/s12045-014-0039-5
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DOI: https://doi.org/10.1007/s12045-014-0039-5