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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds

BuchKartoniert, Paperback
148 Seiten
Englisch
Springererschienen am02.10.2011Softcover reprint of the original 1st ed. 1987
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.mehr
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Produkt

KlappentextIn 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.
Details
ISBN/GTIN978-1-4612-9105-3
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2011
Erscheinungsdatum02.10.2011
AuflageSoftcover reprint of the original 1st ed. 1987
Seiten148 Seiten
SpracheEnglisch
Gewicht254 g
IllustrationenVIII, 148 p.
Artikel-Nr.18226287

Inhalt/Kritik

Inhaltsverzeichnis
1 Groups.- 2 Graphs.- 3 Chemical Compounds.- 4 Asymptotic Evaluation of the Number of Combinations.- The Legacy of Pólya´s Paper: Fifty Years of Pólya Theory.- References.mehr

Autor

Georg(e) Pólya, born in Budapest, December 13, 1887. Georg(e) Pólya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Göttingen and a short stay in Paris, he received an appointment at the ETH in Zürich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He also worked in conformal mappings, potential theory, boundary value problems, and isoperimetric problems in mathematical physics, as well as heuristics late in his career. When Pólya left Europe in 1940, he first went to Brown University, then two years later to Stanford, where he remained until his death on September 7, 1985.
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