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Author: Georg Polya
Publisher: Springer Science & Business Media
ISBN: 1461246644
Category : Mathematics
Languages : en
Pages : 155
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Book Description
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
Author: Georg Polya
Publisher: Springer Science & Business Media
ISBN: 1461246644
Category : Mathematics
Languages : en
Pages : 155
Get Book Here
Book Description
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
Author: George Pólya
Publisher:
ISBN: 9783540964131
Category : Combinatorial enumeration problems
Languages : en
Pages : 148
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Book Description
Author: Carlos Rodríguez Lucatero
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
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Book Description
In this chapter, I will talk about some of the enumerative combinatorics problems that have interested researchers during the last decades. For some of those enumeration problems, it is possible to obtain closed mathematical expressions, and for some other it is possible to obtain an estimation by the use of asymptotic methods. Some of the methods used in both cases will be covered in this chapter as well as some application of graph enumeration in different fields. An overview about the enumeration of trees will be given as an example of combinatorial problem solved in a closed mathematical form. Similarly, the problem of enumeration of regular graphs will be discussed as an example of combinatorial enumeration for which it is hard to obtain a closed mathematical form solution and apply the asymptotic estimation method used frequently in analytic combinatorics for this end. An example of application of the enumerative combinatorics for obtaining a result of applicability criteria of selection nodes in a virus spreading control problem will be given as well.
Author: Miklós Bóna
Publisher:
ISBN: 9789814335249
Category : Electronic books
Languages : en
Pages : 567
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Book Description
Author: Robert Martin Nemba
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659150500
Category :
Languages : en
Pages : 192
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Book Description
Traditional methods for counting position isomers, meso and enantiomeric structures of organic compounds are costumarily based on the classical method of group action leading to the determination of a cycle index convertible into a counting polynomial. The innovative approach presented in this book considers a homopolysubstitution as a Young's Partition including combinations of mono-, gem di- and gem tri-substitutions which are distributed in distinct ways among numerous carbon atoms. The resulting arrangements obtained are used to build up algorithms for enumerating permutomers, meso isomers and enantiomers of series of homopolysubstituted n-alkanes (HPSNAs) with any size. This vision shows the close link existing between stereochemistry and combinatorics and provides new mathematical solutions that should be useful to students, teachers, researchers and professionals in chemistry and biochemistry or to anyone else who may utilize such pattern inventories for isomer enumeration, structural analyses, molecular design or other chemical investigations.
Author: Miklós Bóna
Publisher:
ISBN: 9789812773074
Category : Electronic books
Languages : en
Pages : 489
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Book Description
Author: Sean Thomas
Publisher:
ISBN:
Category : Graph theory
Languages : en
Pages : 48
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Book Description
Author: Shinsaku Fujita
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110728230
Category : Science
Languages : en
Pages : 529
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Book Description
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. In his 2015 book, Fujita developed a new stereoisogram approach that provided theoretical framework for mathematical aspects of modern stereochemistry. This new edition includes a new chapter on Computer-Oriented Representations developed by the author based on Groups, Algorithms, Programming (GAP) system.
Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119058619
Category : Computers
Languages : en
Pages : 296
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Book Description
Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.
Author: R.L. Graham
Publisher: Elsevier
ISBN: 044488002X
Category : Business & Economics
Languages : en
Pages : 1283
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Book Description
