Tools And Fundamental Constructions Of Combinatorial Mathematics
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Tools And Fundamental Constructions Of Combinatorial Mathematics
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Author : Heinz Lüneburg
language : en
Publisher:
Release Date : 1989
Tools And Fundamental Constructions Of Combinatorial Mathematics written by Heinz Lüneburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Combinatorial analysis categories.
Combinatorial Designs
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Author : Douglas Stinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Combinatorial Designs written by Douglas Stinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Mathematics categories.
Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applied mathematics, combinatorics, and applied statistics will find the book an essential resource.
Lessons In Enumerative Combinatorics
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Author : Ömer Eğecioğlu
language : en
Publisher: Springer Nature
Release Date : 2021-05-13
Lessons In Enumerative Combinatorics written by Ömer Eğecioğlu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-13 with Mathematics categories.
This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.
Foundations And Methods In Combinatorial And Statistical Data Analysis And Clustering
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Author : Israël César Lerman
language : en
Publisher: Springer
Release Date : 2016-03-24
Foundations And Methods In Combinatorial And Statistical Data Analysis And Clustering written by Israël César Lerman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-24 with Computers categories.
This book offers an original and broad exploration of the fundamental methods in Clustering and Combinatorial Data Analysis, presenting new formulations and ideas within this very active field. With extensive introductions, formal and mathematical developments and real case studies, this book provides readers with a deeper understanding of the mutual relationships between these methods, which are clearly expressed with respect to three facets: logical, combinatorial and statistical. Using relational mathematical representation, all types of data structures can be handled in precise and unified ways which the author highlights in three stages: Clustering a set of descriptive attributes Clustering a set of objects or a set of object categories Establishing correspondence between these two dual clusterings Tools for interpreting the reasons of a given cluster or clustering are also included. Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering will be a valuable resource for students and researchers who are interested in the areas of Data Analysis, Clustering, Data Mining and Knowledge Discovery.
Combinatorics And Reasoning
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Author : Carolyn A. Maher
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-29
Combinatorics And Reasoning written by Carolyn A. Maher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-29 with Education categories.
Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.
Handbook Of Combinatorial Designs
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Author : Charles J. Colbourn
language : en
Publisher: CRC-Press
Release Date : 1996-02-21
Handbook Of Combinatorial Designs written by Charles J. Colbourn and has been published by CRC-Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-21 with Mathematics categories.
This comprehensive, accessible reference contains all the facts on combinatorial designs. It includes constructions of designs, existence results and properties of designs. Organized into six main parts, The CRC Handbook of Combinatorial Designs covers block design; orthogonal arrays and latin squares; pairwise balanced designs; association schemes; mappings and sequencings; costas arrays; factorial designs; partial geometries; extensive applications of design theory; experimental design; coding theory; cryptography; and general reference tools used for design theory. Although the text emphasizes basic information on combinatorial design, it includes material at the research frontier, maintaining a balance of topics for those actively involved in research.
A First Course In Combinatorial Mathematics
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Author : Ian Anderson (Ph. D.)
language : en
Publisher:
Release Date : 1989
A First Course In Combinatorial Mathematics written by Ian Anderson (Ph. D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Now in a new second edition, this volume presents a clear and concise treatment of an increasingly important branch of mathematics. A unique introductory survey complete with easy-to-understand examples and sample problems, this text includes information on such basic combinatorial tools as recurrence relations, generating functions, incidence matrices, and the non-exclusion principle. It also provides a study of block designs, Steiner triple systems, and expanded coverage of the marriage theorem, as well as a unified account of three important constructions which are significant in coding theory.
A First Course In Enumerative Combinatorics
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Author : Carl G. Wagner
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-29
A First Course In Enumerative Combinatorics written by Carl G. Wagner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-29 with Education categories.
A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erdős number is 2.
Handbook Of Combinatorial Designs
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Author : C. J. Colbourn
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2006-11-02
Handbook Of Combinatorial Designs written by C. J. Colbourn and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.
Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results. Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory. New to the Second Edition An introductory part that provides a general overview and a historical perspective of the area New chapters on the history of design theory, various codes, bent functions, and numerous types of designs Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices Nearly 2,200 references in a single bibliographic section Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline. The author maintains a website with more information.
Graphs Networks And Algorithms
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Author : Dieter Jungnickel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Graphs Networks And Algorithms written by Dieter Jungnickel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed