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)

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
Creator
Contributor
Author
Provider
Subject
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 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
Member of
http://library.link/vocab/creatorName
Stanley, Richard P
Image bit depth
0
LC call number
QA164-167.2
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)
Instantiates
Publication
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 q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix-Tree 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
10.1007/978-3-319-77173-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-77173-1
Label
Algebraic Combinatorics : Walks, Trees, Tableaux, and More, by Richard P. Stanley, (electronic resource)
Publication
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 q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix-Tree 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
10.1007/978-3-319-77173-1
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-77173-1

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