The Combinatories of the Permutation Enumeration of Wreath Products Between Cyclic and Symmetric Groups PDF Download
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Author: Jennifer D. Wagner
Publisher:
ISBN:
Category :
Languages : en
Pages : 366
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Author: Jennifer D. Wagner
Publisher:
ISBN:
Category :
Languages : en
Pages : 366
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Author: Jeffrey Remmel
Publisher: Birkhäuser
ISBN: 3319236180
Category : Mathematics
Languages : en
Pages : 297
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Book Description
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
Author: Steve Linton
Publisher: Cambridge University Press
ISBN: 1139488848
Category : Mathematics
Languages : en
Pages : 353
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Book Description
A mixture of survey and research articles by leading experts that will be of interest to specialists in permutation patterns and other researchers in combinatorics and related fields. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.
Author: Joseph P. S. Kung
Publisher: Cambridge University Press
ISBN: 052188389X
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.
Author: Desiree Anne Beck
Publisher:
ISBN:
Category :
Languages : en
Pages : 402
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Author: Peter Jephson Cameron
Publisher: Cambridge University Press
ISBN: 9780521457613
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Author: Richard P. Stanley
Publisher: Springer
ISBN: 3319771736
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added. From reviews of the first edition: “This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics ... . Stanley’s emphasis on ‘gems’ unites all this —he chooses his material to excite students and draw them into further study. ... Summing Up: Highly recommended. Upper-division undergraduates and above.” —D. V. Feldman, Choice, Vol. 51(8), April, 2014
Author: Stanley Gill Williamson
Publisher: Courier Corporation
ISBN: 9780486420769
Category : Mathematics
Languages : en
Pages : 548
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Book Description
Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.
Author: Visvanatha Krishnamurthy
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 528
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Author: Thomas Langley
Publisher:
ISBN:
Category :
Languages : en
Pages : 404
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Book Description
