This lecture note covers the
following topics: What is Combinatorics, Permutations and Combinations,
Inclusion-Exclusion-Principle and Mobius Inversion, Generating Functions,
Partitions, Partially Ordered Sets and Designs.
This book will bring enjoyment to many future generations of
mathematicians and aspiring mathematicians as they are exposed to the beauties
and pleasures of enumerative combinatorics. Topics covered includes: What is
Enumerative Combinatorics, Sieve Methods, Partially Ordered Sets, Rational
Generating Functions, Graph Theory Terminology
of this note is to give students a broad exposure to combinatorial mathematics,
using applications to emphasize fundamental concepts and techniques. Topics
covered includes: Introduction to Combinatorics, Strings, Sets, and Binomial
Coefficients, Induction, Combinatorial Basics, Graph Theory, Partially Ordered
Sets, Generating Functions, Recurrence Equations , Probability, Applying
Probability to Combinatorics, Combinatorial Applications of Network Flows,
Polya’s Enumeration Theorem.
Author(s): Mitchel T. Keller and William T. Trotter
This book covers the following topics: Fibonacci Numbers From a
Cominatorial Perspective, Functions,Sequences,Words,and Distributions, Subsets
with Prescribed Cardinality, Sequences of Two Sorts of Things with Prescribed
Frequency, Sequences of Integers with Prescribed Sum, Combinatorics and
Probability, Binary Relations, Factorial Polynomials, The Calculus of Finite
Differences, Principle of Inclusion and Exclusions.
The authors give full coverage of the underlying
mathematics and give a thorough treatment of both classical and modern
applications of the theory. The text is complemented with exercises, examples,
appendices and notes throughout the book to aid understanding. Major topics covered includes: Symbolic Methods, Complex Asymptotics, Random Structures, Auxiliary Elementary Notions and Basic Complex Analysis.