An Invitation to Combinatorics

Shahriar Shahriari

• Publisher: Cambridge University Press
• Year: 2021
• Print ISBN:
  9781108476546
• eBook ISBN:
  9781108756426
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• Acknowledgments
• Introduction
• 1 Induction and Recurrence Relations
• 2 The Pigeonhole Principle and Ramsey Theory
• 3 Counting, Probability, Balls and Boxes
• Collaborative Mini-project 1: Counting Monochromatic Triangles
• Collaborative Mini-project 2: Binomial Coefficients
• Collaborative Mini-project 3: Stirling Numbers
• 4 Permutations and Combinations
• 5 Binomial and Multinomial Coefficients
• 6 Stirling Numbers
• 7 Integer Partitions
• Collaborative Mini-project 4: Generating Functions
• Collaborative Mini-project 5: Graphic Sequences and Planar Graphs
• Collaborative Mini-project 6: Connectivity of Graphs
• 8 The Inclusion–Exclusion Principle
• 9 Generating Functions
• Interregnum: Counting Table Completed
• Collaborative Mini-project 7: Ming–Catalan Numbers
• Collaborative Mini-project 8: Sperner's Theorem
• 10 Graph Theory
• Collaborative Mini-project 9: Cayley's Tree Formula
• Collaborative Mini-project 10: Incidence Matrices and Bipartite Graphs
• 11 Posets, Matchings, and Boolean Lattices
• Appendix A Short Answers for Warm-Up Problems
• Appendix B Hints for Selected Problems
• Appendix C Short Answers for Selected Problems
• Appendix D Complete Solutions for Selected Problems
• Bibliography
• Index