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Author: Steven Roman Publisher: Birkhäuser ISBN: 3319221442 Category : Mathematics Languages : en Pages : 127
Book Description
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.” - From the foreword by Richard Stanley
Author: Steven Roman Publisher: Birkhäuser ISBN: 3319221442 Category : Mathematics Languages : en Pages : 127
Book Description
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.” - From the foreword by Richard Stanley
Author: James Haglund Publisher: American Mathematical Soc. ISBN: 0821844113 Category : Mathematics Languages : en Pages : 178
Book Description
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
Author: Alex Degtyarev Publisher: Walter de Gruyter ISBN: 3110258420 Category : Mathematics Languages : en Pages : 412
Book Description
This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces. An emphasis is given to various applications of the theory to a few related areas, most notably singular plane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The approach relies on a close relation between trigonal curves/elliptic surfaces, a certain class of ribbon graphs, and subgroups of the modular group, which provides a combinatorial framework for the study of geometric objects. A brief summary of the necessary auxiliary results and techniques used and a background of the principal problems dealt with are included in the text. The book is intended to researchers and graduate students in the field of topology of complex and real algebraic varieties.
Author: Richard Johnsonbaugh Publisher: Prentice Hall ISBN: 0131593188 Category : Computer science Languages : en Pages : 785
Book Description
For a one- or two-term introductory course in discrete mathematics. Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.
Author: David R. Mazur Publisher: American Mathematical Society ISBN: 1470472864 Category : Mathematics Languages : en Pages : 411
Book Description
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.
Author: Sung-Hyuk Cha Publisher: Cha Academy llc ISBN: 1735168009 Category : Computers Languages : en Pages : 798
Book Description
The intended readership includes both undergraduate and graduate students majoring in computer science as well as researchers in the computer science area. The book is suitable either as a textbook or as a supplementary book in algorithm courses. Over 400 computational problems are covered with various algorithms to tackle them. Rather than providing students simply with the best known algorithm for a problem, this book presents various algorithms for readers to master various algorithm design paradigms. Beginners in computer science can train their algorithm design skills via trivial algorithms on elementary problem examples. Graduate students can test their abilities to apply the algorithm design paradigms to devise an efficient algorithm for intermediate-level or challenging problems. Key Features: Dictionary of computational problems: A table of over 400 computational problems with more than 1500 algorithms is provided. Indices and Hyperlinks: Algorithms, computational problems, equations, figures, lemmas, properties, tables, and theorems are indexed with unique identification numbers and page numbers in the printed book and hyperlinked in the e-book version. Extensive Figures: Over 435 figures illustrate the algorithms and describe computational problems. Comprehensive exercises: More than 352 exercises help students to improve their algorithm design and analysis skills. The answers for most questions are available in the accompanying solution manual.
Author: Martin Grohe Publisher: American Mathematical Soc. ISBN: 0821849433 Category : Mathematics Languages : en Pages : 529
Book Description
This volume contains the proceedings of the AMS-ASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5-8, 2009, in Washington, DC. Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 0-1 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics. This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 0-1 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.
Author: Rolf Karlsson Publisher: Springer Science & Business Media ISBN: 9783540194873 Category : Computers Languages : en Pages : 274
Book Description
The papers in this volume were presented at the 1st Scandinavian Workshop on Algorithm Theory held July 5-8, 1988 in Halmstad, Sweden. The contributions present original research in areas related to algorithm theory, including data structures, computational geometry, and computational complexity. In addition to the selected papers the proceedings include invited papers from I. Munro, K. Mehlhorn, M. Overmars, and D. Wood.
Author: Steven Roman
Author: Steven Roman
Author: James Haglund
Author: Alex Degtyarev
Author: Richard Johnsonbaugh
Author: David R. Mazur
Author: Sung-Hyuk Cha
Author: Martin Grohe
Author: Muhammad Ali McBeth
Author: Rolf Karlsson
Author: Richard P. Stanley