Combinatorics '90
Combinatorics '90

Author: A. Barlotti

Publisher: Elsevier

Published: 1992-08-17

Total Pages: 577

ISBN-13: 0080867928

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This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

Algebraic Combinatorics on Words
Algebraic Combinatorics on Words

Author: M. Lothaire

Publisher: Cambridge University Press

Published: 2002-04-18

Total Pages: 536

ISBN-13: 9780521812207

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Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.

Combinatorics
Combinatorics

Author: N. Ya. Vilenkin

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 313

ISBN-13: 1483266117

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Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics.

Algebraic Combinatorics
Algebraic Combinatorics

Author: Chris Godsil

Publisher: Routledge

Published: 2017-10-19

Total Pages: 368

ISBN-13: 1351467514

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This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

EUROCODE '90
EUROCODE '90

Author: Gerard Cohen

Publisher: Springer Science & Business Media

Published: 1991-07-24

Total Pages: 410

ISBN-13: 9783540543039

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This book presents a selection of the papers presented at EUROCODE '90, the symposium on coding theory held in Udine, Italy, November 1990. It gives the state of the art on coding in Europe and ranges from theoretical top- ics like algebraic geometry and combinatorial coding to applications like modulation, real-space decoding and VLSI implementation. The book is divided into eight sections: - Algebraic codes - Combinatorial codes - Geometric codes - Protection of information - Convolutional codes - Information theory - Modulation - Applications of coding. Five of the sections are introduced by an invited contribution.

Surveys in Combinatorics, 1997
Surveys in Combinatorics, 1997

Author: Rosemary Bailey

Publisher: Cambridge University Press

Published: 1997

Total Pages: 356

ISBN-13: 0521598400

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The invited lectures given at the 16th. British Combinatorial Conference, July 1997 at Queen Mary and Westfield College.

Counting and Configurations
Counting and Configurations

Author: Jiri Herman

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 402

ISBN-13: 1475739257

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This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.

An Invitation to Analytic Combinatorics
An Invitation to Analytic Combinatorics

Author: Stephen Melczer

Publisher: Springer Nature

Published: 2020-12-22

Total Pages: 418

ISBN-13: 3030670805

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This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

Finite Geometry and Combinatorics
Finite Geometry and Combinatorics

Author: Albrecht Beutelspacher

Publisher: Cambridge University Press

Published: 1993

Total Pages: 428

ISBN-13: 9780521448505

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Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.

Surveys in Combinatorics, 2001
Surveys in Combinatorics, 2001

Author: J. W. P. Hirschfeld

Publisher: Cambridge University Press

Published: 2001-07-05

Total Pages: 324

ISBN-13: 9780521002707

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This volume contains the invited talks from the 18th British Combinatorial Conference, held in 2001.