Bijective Combinatorics
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Bijective Combinatorics
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Author : Nicholas Loehr
language : en
Publisher: CRC Press
Release Date : 2011-02-10
Bijective Combinatorics written by Nicholas Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Computers categories.
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
Combinatorics
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Author : Nicholas Loehr
language : en
Publisher: CRC Press
Release Date : 2017-08-10
Combinatorics written by Nicholas Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Mathematics categories.
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Combinatorics A Guided Tour
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Author : David R. Mazur
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-19
Combinatorics A Guided Tour written by David R. Mazur 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 2020-02-19 with Education categories.
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.
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.
Formal Power Series And Algebraic Combinatorics
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Author : Daniel Krob
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Formal Power Series And Algebraic Combinatorics written by Daniel Krob 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 2013-03-09 with Mathematics categories.
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Percolation On Triangulations A Bijective Path To Liouville Quantum Gravity
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Author : Olivier Bernardi
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27
Percolation On Triangulations A Bijective Path To Liouville Quantum Gravity written by Olivier Bernardi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.
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Combinatorics
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Author : Nicholas Loehr
language : en
Publisher: CRC Press
Release Date : 2017-08-10
Combinatorics written by Nicholas Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-10 with Mathematics categories.
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Handbook Of Enumerative Combinatorics
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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-03-24
Handbook Of Enumerative Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.
Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
Bijective Combinatorial Methods In The Comparison Of Optimal Algorithms
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Author : Laura Anne Bloom
language : en
Publisher:
Release Date : 1992
Bijective Combinatorial Methods In The Comparison Of Optimal Algorithms written by Laura Anne Bloom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Combinatorics Of Permutations
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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2004-06-25
Combinatorics Of Permutations written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-25 with Mathematics categories.
WINNER of a CHOICE Outstanding Academic Title Award for 2006! As linear orders, as elements of the symmetric group, modeled by matrices, modeled by graphs...permutations are omnipresent in modern combinatorics. They are omnipresent but also multifaceted, and while several excellent books explore particular aspects of the subject, no one book has covered them all. Even the classic results are scattered in various resources. Combinatorics of Permutations offers the first comprehensive, up to date treatment of both enumerative and extremal combinatorics and looks at permutation as linear orders and as elements of the symmetric group. The author devotes two full chapters to the young but active area of pattern avoidance. He explores the quest for the Stanley-Wilf conjecture and includes the recent and spectacular Marcus-Tardos proof of this problem. He examines random permutations and Standard Young Tableaux and provides an overview of the very rich algebraic combinatorics of permutations. The final chapter takes an in-depth look at combinatorial sorting algorithms. The author's style is relaxed, entertaining, and clearly reflects his enthusiasm for the "serious fun" the subject holds. Filled with applications from a variety of fields and exercises that draw upon recent research results, this book serves equally well as a graduate-level text and a reference for combinatorics researchers.