Notes on Counting: An Introduction to Enumerative Combinatorics
Title | Notes on Counting: An Introduction to Enumerative Combinatorics PDF eBook |
Author | Peter J. Cameron |
Publisher | Cambridge University Press |
Pages | 235 |
Release | 2017-06-21 |
Genre | Mathematics |
ISBN | 1108279325 |
Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield–Pólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.
Enumerative Combinatorics
Title | Enumerative Combinatorics PDF eBook |
Author | Charalambos A. Charalambides |
Publisher | CRC Press |
Pages | 632 |
Release | 2018-10-08 |
Genre | Business & Economics |
ISBN | 1482296314 |
Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.
Introduction to Enumerative and Analytic Combinatorics
Title | Introduction to Enumerative and Analytic Combinatorics PDF eBook |
Author | Miklos Bona |
Publisher | CRC Press |
Pages | 555 |
Release | 2015-09-18 |
Genre | Computers |
ISBN | 1482249103 |
Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat
Enumerative Combinatorics: Volume 1
Title | Enumerative Combinatorics: Volume 1 PDF eBook |
Author | Richard P. Stanley |
Publisher | Cambridge University Press |
Pages | 641 |
Release | 2012 |
Genre | Mathematics |
ISBN | 1107015421 |
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.
Notes on Introductory Combinatorics
Title | Notes on Introductory Combinatorics PDF eBook |
Author | George Polya |
Publisher | Springer Science & Business Media |
Pages | 202 |
Release | 2013-11-27 |
Genre | Science |
ISBN | 1475711018 |
In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.
Counting: The Art of Enumerative Combinatorics
Title | Counting: The Art of Enumerative Combinatorics PDF eBook |
Author | George E. Martin |
Publisher | Springer Science & Business Media |
Pages | 263 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 1475748787 |
This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.
Combinatorics: The Art of Counting
Title | Combinatorics: The Art of Counting PDF eBook |
Author | Bruce E. Sagan |
Publisher | American Mathematical Soc. |
Pages | 304 |
Release | 2020-10-16 |
Genre | Education |
ISBN | 1470460327 |
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.