Basic methods
When we add and when we subtract
When we multiply
When we divide
Applications of basic counting principles
The pigeonhole principle
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Applications of basic methods
Multisets and compositions
Set partitions
Partitions of integers
The inclusion-exclusion principle
The twelvefold way
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Generating functions
Power series
Warming up: Solving recurrence relations
Products of generating functions
Compositions of generating functions
A different type of generating functions
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
TOPICS
Counting permutations
Eulerian numbers
The cycle structure of permutations
Cycle structure and exponential generating functions
Inversions
Advanced applications of generating functions to permutation enumeration
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Counting graphs
Trees and forests
Graphs and functions
When the vertices are not freely labeled
Graphs on colored vertices
Graphs and generating functions
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Extremal combinatorics
Extremal graph theory
Hypergraphs
Something is more than nothing: Existence proofs
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
AN ADVANCED METHOD
Analytic combinatorics
Exponential growth rates
Polynomial precision
More precise asymptotics
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
SPECIAL TOPICS
Symmetric structures
Designs
Finite projective planes
Error-correcting codes
Counting symmetric structures
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Sequences in combinatorics
Unimodality
Log-concavity
The real zeros property
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Counting magic squares and magic cubes
A distribution problem
Magic squares of fixed size
Magic squares of fixed line sum
Why magic cubes are different
Notes
Chapter review
Exercises
Solutions to exercises
Supplementary exercises
Appendix: The method of mathematical induction
Weak induction
Strong induction
Biography
Miklós Bóna received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an Editor-in-Chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.
