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The Resource Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource)
Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource)
Resource Information
The item Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 MatrixTree 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 onesemester 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 steppingstone 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. Upperdivision undergraduates and above.” —D. V. Feldman, Choice, Vol. 51(8), April, 2014
 Language
 eng
 Edition
 2nd ed. 2018.
 Extent
 1 online resource
 Contents

 Updated preface to the first edition
 Preface to the second edition.Basic notation
 1. Walks in graphs
 2. Cubes and the Radon transform
 3. Random walks
 4. The Sperner property
 5. Group actions on boolean algebras
 6. Young diagrams and qbinomial coefficients
 7. Enumeration under group action
 8. A glimpse of Young tableaux
 Appendix. The RSK algorithm
 Appendix. Plane partitions
 9. The MatrixTree theorem
 Appendix. Three elegant combinatorial proofs
 10. Eulerian diagraphs and oriented trees
 11. Cycles, bonds, and electrical networks
 12. A glimpse of combinatorial commutative algebra
 13. Miscellaneous gems of algebraic combinatorics
 Hints and comments
 Bibliography
 Index
 Isbn
 9783319771731
 Label
 Algebraic Combinatorics : Walks, Trees, Tableaux, and More
 Title
 Algebraic Combinatorics
 Title remainder
 Walks, Trees, Tableaux, and More
 Statement of responsibility
 by Richard P. Stanley
 Language
 eng
 Summary
 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 MatrixTree 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 onesemester 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 steppingstone 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. Upperdivision undergraduates and above.” —D. V. Feldman, Choice, Vol. 51(8), April, 2014
 http://library.link/vocab/creatorName
 Stanley, Richard P
 Image bit depth
 0
 LC call number
 QA164167.2
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Undergraduate Texts in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Combinatorial analysis
 Graph theory
 Mathematics
 Combinatorics
 Graph Theory
 Label
 Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Updated preface to the first edition  Preface to the second edition.Basic notation  1. Walks in graphs  2. Cubes and the Radon transform  3. Random walks  4. The Sperner property  5. Group actions on boolean algebras  6. Young diagrams and qbinomial coefficients  7. Enumeration under group action  8. A glimpse of Young tableaux  Appendix. The RSK algorithm  Appendix. Plane partitions  9. The MatrixTree theorem  Appendix. Three elegant combinatorial proofs  10. Eulerian diagraphs and oriented trees  11. Cycles, bonds, and electrical networks  12. A glimpse of combinatorial commutative algebra  13. Miscellaneous gems of algebraic combinatorics  Hints and comments  Bibliography  Index
 Dimensions
 unknown
 Edition
 2nd ed. 2018.
 Extent
 1 online resource
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319771731
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319771731
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319771731
 Label
 Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Updated preface to the first edition  Preface to the second edition.Basic notation  1. Walks in graphs  2. Cubes and the Radon transform  3. Random walks  4. The Sperner property  5. Group actions on boolean algebras  6. Young diagrams and qbinomial coefficients  7. Enumeration under group action  8. A glimpse of Young tableaux  Appendix. The RSK algorithm  Appendix. Plane partitions  9. The MatrixTree theorem  Appendix. Three elegant combinatorial proofs  10. Eulerian diagraphs and oriented trees  11. Cycles, bonds, and electrical networks  12. A glimpse of combinatorial commutative algebra  13. Miscellaneous gems of algebraic combinatorics  Hints and comments  Bibliography  Index
 Dimensions
 unknown
 Edition
 2nd ed. 2018.
 Extent
 1 online resource
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319771731
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319771731
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319771731
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