Combinatorial Enumeration Of Groups Graphs And Chemical Compounds

Author : Georg Polya,R.C. Read
Publisher : Springer Science & Business Media
Page : 155 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461246640

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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds by Georg Polya,R.C. Read Pdf

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,Ronald C. Read
Publisher : Unknown
Page : 148 pages
File Size : 46,6 Mb
Release : 1987-01-01
Category : Combinatorial enumeration problems
ISBN : 3540964134

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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds by George Pólya,Ronald C. Read Pdf

Author : T H Ku,E K Lloyd,Z M Wang,H P Yap
Publisher : World Scientific
Page : 288 pages
File Size : 45,7 Mb
Release : 1993-09-23
Category : Electronic
ISBN : 9789814552622

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Combinatorics and Graph Theory by T H Ku,E K Lloyd,Z M Wang,H P Yap Pdf

This volume contains selected papers presented at the Spring School and International Conference on Combinatorics. Topics discussed include: Enumeration, Design, Graphs, Hypergraphs and Combinatorial Optimization, etc. Covering a broad range, this book should appeal to a wide spectrum of researchers in combinatorics and graph theory. Contents:Partial n-Solution to the Modular n-Queens Problem II (M R Chen et al)Power-Type Generating Functions and Asymptotic Expansions (L C Hsu)Enumeration Using Cycle Indices and Marks (E K Lloyd)Design Patterns of Incomplete Block Designs for Parallel Line Assays (P D Puri & L R Gupta)Research about the Structure of EGD/(2t-1) — PBIB Designs (J Y Xu)Strongly Extendable Graphs I (Z Q Chen)Group Generation of Self-Complementary Graphs (R Figueroa & R E Guidici)Decomposition of Kn into Degenerate Graphs (R Klein & J Schönheim)Homo-morphisms on n-Dimensional Line Digraphs (X L Li & F J Zhang)Total Chromatic Number of Graphs G having Maximum Degree |G|– 3 (H P Yap)On Optimal Network with Quasi-Full Steiner Topology (J Y Ding & G D Song)A General Scheme for Solving Linear Complementarity Problems in the Setting of Oriented Matroids (T Terlaky & Z-M Wang)A Linear Programming Interpretation of Lemke's Scheme I (R Zhou)and other papers Readership: Mathematicians. keywords:

Author : Shinsaku Fujita
Publisher : Walter de Gruyter GmbH & Co KG
Page : 529 pages
File Size : 46,8 Mb
Release : 2021-09-20
Category : Science
ISBN : 9783110728231

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Mathematical Stereochemistry by Shinsaku Fujita Pdf

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 : Shinsaku Fujita
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642766961

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Symmetry and Combinatorial Enumeration in Chemistry by Shinsaku Fujita Pdf

This book is written to introduce a new approach to stereochemical problems and to combinatorial enumerations in chemistry. This approach is based on group the ory, but different from conventional ways adopted by most textbooks on chemical group theory. The difference sterns from their starting points: conjugate subgroups and conjugacy classes. The conventional textbooks deal with linear representations and character ta bles of point groups. This fact implies that they lay stress on conjugacy classesj in fact, such group characters are determined for the respective conjugacy classes. This approach is versatile, since conjugacy classes can be easily obtained by ex amining every element of a group. It is unnecessary to know the group-subgroup relationship of the group, which is not always easy to obtain. The same situa tion is true for chemical enumerations, though these are founded on permutation groups. Thus, the P6lya-Redfield theorem (1935 and 1927) uses a cycle index that is composed of terms associated with conjugacy classes.

Author : Russell Merris
Publisher : John Wiley & Sons
Page : 580 pages
File Size : 44,5 Mb
Release : 2003-08-15
Category : Mathematics
ISBN : 9780471262961

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Combinatorics by Russell Merris Pdf

A mathematical gem–freshly cleaned and polished This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course. Features retained from the first edition: Lively and engaging writing style Timely and appropriate examples Numerous well-chosen exercises Flexible modular format Optional sections and appendices Highlights of Second Edition enhancements: Smoothed and polished exposition, with a sharpened focus on key ideas Expanded discussion of linear codes New optional section on algorithms Greatly expanded hints and answers section Many new exercises and examples

Author : Danail Bonchev,D. H. Rouvray
Publisher : Taylor & Francis
Page : 268 pages
File Size : 53,8 Mb
Release : 1995
Category : Science
ISBN : 2884490345

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Chemical Group Theory by Danail Bonchev,D. H. Rouvray Pdf

First Published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Oleg N. Temkin,Andrew V. Zeigarnik,D.G. Bonchev
Publisher : CRC Press
Page : 297 pages
File Size : 51,8 Mb
Release : 2020-07-24
Category : Science
ISBN : 9781000102666

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Chemical Reaction Networks by Oleg N. Temkin,Andrew V. Zeigarnik,D.G. Bonchev Pdf

Over the last decade, increased attention to reaction dynamics, combined with the intensive application of computers in chemical studies, mathematical modeling of chemical processes, and mechanistic studies has brought graph theory to the forefront of research. It offers an advanced and powerful formalism for the description of chemical reactions and their intrinsic reaction mechanisms. Chemical Reaction Networks: A Graph-Theoretical Approach elegantly reviews and expands upon graph theory as applied to mechanistic theory, chemical kinetics, and catalysis. The authors explore various graph-theoretical approaches to canonical representation, numbering, and coding of elementary steps and chemical reaction mechanisms, the analysis of their topological structure, the complexity estimation, and classification of reaction mechanisms. They discuss topologically distinctive features of multiroute catalytic and noncatalytic and chain reactions involving metal complexes. With it's careful balance of clear language and mathematical rigor, the presentation of the authors' significant original work, and emphasis on practical applications and examples, Chemical Reaction Networks: A Graph Theoretical Approach is both an outstanding reference and valuable tool for chemical research.

Author : R.L. Graham,Martin Grötschel,László Lovász
Publisher : Elsevier
Page : 1283 pages
File Size : 45,5 Mb
Release : 1995-12-11
Category : Business & Economics
ISBN : 9780444880024

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Handbook of Combinatorics by R.L. Graham,Martin Grötschel,László Lovász Pdf

Author : Robin Wilson,John J. Watkins
Publisher : OUP Oxford
Page : 392 pages
File Size : 50,8 Mb
Release : 2013-06-27
Category : Mathematics
ISBN : 9780191630620

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Combinatorics: Ancient & Modern by Robin Wilson,John J. Watkins Pdf

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

Author : Jean-Loup Faulon,Andreas Bender
Publisher : CRC Press
Page : 454 pages
File Size : 52,7 Mb
Release : 2010-04-21
Category : Science
ISBN : 142008299X

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Handbook of Chemoinformatics Algorithms by Jean-Loup Faulon,Andreas Bender Pdf

Unlike in the related area of bioinformatics, few books currently exist that document the techniques, tools, and algorithms of chemoinformatics. Bringing together worldwide experts in the field, the Handbook of Chemoinformatics Algorithms provides an overview of the most common chemoinformatics algorithms in a single source.After a historical persp

Author : Adalbert Kerber
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 49,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662111673

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Applied Finite Group Actions by Adalbert Kerber Pdf

Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

Author : Craig Bauer
Publisher : CRC Press
Page : 718 pages
File Size : 43,8 Mb
Release : 2020-05-14
Category : Mathematics
ISBN : 9780429682896

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Discrete Encounters by Craig Bauer Pdf

Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated

Author : Dusanka Janezic,Ante Milicevic,Sonja Nikolic,Nenad Trinajstic
Publisher : CRC Press
Page : 174 pages
File Size : 42,7 Mb
Release : 2015-04-22
Category : Mathematics
ISBN : 9781498701228

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Graph-Theoretical Matrices in Chemistry by Dusanka Janezic,Ante Milicevic,Sonja Nikolic,Nenad Trinajstic Pdf

Graph-Theoretical Matrices in Chemistry presents a systematic survey of graph-theoretical matrices and highlights their potential uses. This comprehensive volume is an updated, extended version of a former bestseller featuring a series of mathematical chemistry monographs. In this edition, nearly 200 graph-theoretical matrices are included.This sec

Author : François Bergeron,Gilbert Labelle,Pierre Leroux
Publisher : Cambridge University Press
Page : 484 pages
File Size : 52,9 Mb
Release : 1998
Category : Mathematics
ISBN : 0521573238

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Combinatorial Species and Tree-like Structures by François Bergeron,Gilbert Labelle,Pierre Leroux Pdf

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.