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.

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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An Introduction To Symmetric Functions And Their Combinatorics

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Author : Eric S. Egge
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-18

An Introduction To Symmetric Functions And Their Combinatorics written by Eric S. Egge 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 2019-11-18 with Education categories.

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Problem Solving Strategies

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Author : Arthur Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-05-11

Problem Solving Strategies written by Arthur Engel 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 1999-05-11 with Mathematics categories.

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

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Author :
language : en
Publisher: IOS Press
Release Date :

written by and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Algebraic Combinatorics And Applications

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Author : Anton Betten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09

Algebraic Combinatorics And Applications written by Anton Betten 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 2013-11-09 with Mathematics categories.

Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool for researchers and graduate students in discrete mathematics and theoretical computer science.

Hands On Combinatorics

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Author : Brian Hopkins
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-29

Hands On Combinatorics written by Brian Hopkins 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 2025-01-29 with Mathematics categories.

This book provides an active-learning approach to combinatorial reasoning and proof through a thoughtful sequence of low threshold, high ceiling activities. A novel feature is its narrative format, with much of the text written from the perspective of a student working through the material with peers. Furthermore, each chapter includes detailed notes for the instructor such as additional scaffolding, extensions, and notation for more advanced students. The exposition is complemented by over 300 colorful illustrations. The main focus of the book is the study of integer compositions with forays into graph theory and recreational mathematics. Befitting the constructive nature of the book, compositions are represented by trains made up of cars. By physically constructing these objects, students become proficient in hands-on verifications of numerous identities. Developed by a recipient of the MAA's Haimo Award for Distinguished Teaching and used in several teacher professional development workshops and college courses, the book has very modest prerequisites. In particular, no prior experience with symbolic formalism is presumed, allowing this material to be used in multiple classroom settings, from enrichment activities for secondary school students through undergraduate classes in discrete mathematics. The structure of the book also makes it conducive to self-study. Get ready to “build some trains” and explore the enlightening world of combinatorial proofs! Hands-On Combinatorics is a wonderful book, cleverly designed for readers of all mathematical levels. With eye-catching illustrations, Brian Hopkins creates beautiful bijections and clever combinatorial arguments with binomial coefficients, Fibonacci numbers, and beyond. —Arthur T. Benjamin, Harvey Mudd College, co-author of Proofs That Really Count

Solomon Golomb S Course On Undergraduate Combinatorics

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Author : Solomon W. Golomb
language : en
Publisher: Springer Nature
Release Date : 2021-09-13

Solomon Golomb S Course On Undergraduate Combinatorics written by Solomon W. Golomb and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-13 with Mathematics categories.

This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb’s insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study. Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems. Solomon Golomb’s Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book’s many entertaining challenges.

Introduction To Combinatorics

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Author : Walter D. Wallis
language : en
Publisher: CRC Press
Release Date : 2016-12-12

Introduction To Combinatorics written by Walter D. Wallis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Mathematics categories.

What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM