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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds (Paperback, Softcover reprint of the original 1st ed. 1987)
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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds (Paperback, Softcover reprint of the original 1st ed. 1987)
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In 1937 there appeared a paper that was to have a profound
influence on the progress of combinatorial enumeration, both in its
theoretical and applied aspects. Entitled Kombinatorische
Anzahlbest- immungen jUr Gruppen, Graphen und chemische
Verbindungen, it was published in Acta Mathematica, Vol. 68, pp.
145 to 254. Its author, George Polya, was already a mathematician
of considerable stature, well-known for outstanding work in many
branches of mathematics, particularly analysis. The paper in
Question was unusual in that it depended almost entirely on a
single theorem -- the "Hauptsatz" of Section 4 -- a theorem which
gave a method for solving a general type of enumera- tion problem.
On the face of it, this is not something that one would expect to
run to over 100 pages. Yet the range of the applica- tions of the
theorem and of its ramifications was enormous, as Polya clearly
showed. In the various sections of his paper he explored many
applications to the enumeration of graphs, principally trees, and
of chemical isomers, using his theorem to present a comprehen- sive
and unified treatment of problems which had previously been solved,
if at all, only by ad hoc methods. In the final section he
investigated the asymptotic properties of these enumerational
results, bringing to bear his formidable insight as an analyst.
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