Constructive Combinatorics

Constructive Combinatorics
Title Constructive Combinatorics PDF eBook
Author Dennis Stanton
Publisher Springer Science & Business Media
Pages 194
Release 2012-12-06
Genre Mathematics
ISBN 1461249686

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The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science majors, with an occasional engineering student. Several graduate students in computer science also attend. At Minnesota, Constructive Combinatorics is the third quarter of a three quarter sequence. The fIrst quarter, Enumerative Combinatorics, is at the level of the texts by Bogart [Bo], Brualdi [Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this course. The second quarter, Graph Theory and Optimization, is not a prerequisite. We assume that the students are familiar with the techniques of enumeration: basic counting principles, generating functions and inclusion/exclusion. This course evolved from a course on combinatorial algorithms. That course contained a mixture of graph algorithms, optimization and listing algorithms. The computer assignments generally consisted of testing algorithms on examples. While we felt that such material was useful and not without mathematical content, we did not think that the course had a coherent mathematical focus. Furthermore, much of it was being taught, or could have been taught, elsewhere. Graph algorithms and optimization, for instance, were inserted into the graph theory course where they naturally belonged. The computer science department already taught some of the material: the simpler algorithms in a discrete mathematics course; effIciency of algorithms in a more advanced course.

Constructive Combinatorics

Constructive Combinatorics
Title Constructive Combinatorics PDF eBook
Author Earl Glen Whitehead
Publisher
Pages 140
Release 1973
Genre Combinatorial analysis
ISBN

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Combinatorics and Graph Theory

Combinatorics and Graph Theory
Title Combinatorics and Graph Theory PDF eBook
Author John Harris
Publisher Springer Science & Business Media
Pages 392
Release 2009-04-03
Genre Mathematics
ISBN 0387797114

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These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Introduction to Combinatorics

Introduction to Combinatorics
Title Introduction to Combinatorics PDF eBook
Author Martin J. Erickson
Publisher John Wiley & Sons
Pages 210
Release 2011-10-24
Genre Mathematics
ISBN 1118030893

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This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Combinatorial Algorithms

Combinatorial Algorithms
Title Combinatorial Algorithms PDF eBook
Author Donald L. Kreher
Publisher CRC Press
Pages 346
Release 2020-09-24
Genre Computers
ISBN 1000141373

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This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as: Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.

Combinatorics: The Art of Counting

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

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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.

ICIAM 91

ICIAM 91
Title ICIAM 91 PDF eBook
Author Robert E. O'Malley
Publisher SIAM
Pages 424
Release 1992-01-01
Genre Mathematics
ISBN 9780898713022

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Proceedings -- Computer Arithmetic, Algebra, OOP.