This PDF covers the
following topics related to Combinatorics : Introduction, Enumeration,
Sequences and the Multiplication Principle, Permutations and Combinations,
Bijections and Double Counting, Estimation, Inclusion-Exclusion, Generating
Functions, Formal Power Series, Generating Functions Redux, Change making,
Compositions, Counting Subsets, Counting Strings, The Probabilistic Method,
Preliminaries, The first moment method, Linearity of expectation,
Alterations, Markov and Chebyshev, Chernoff Bound, Lov´asz Local Lemma,
Extremal Graph Theory, Tur´an’s Theorem, Projective planes, Sidon sets,
Constructing C4-free graphs, Ramsey numbers, Combinatorial Number Theory,
Erd os-Ko-Rado Theorem, Spectral graph theory, Linear Algebra Preliminaries,
The adjacency matrix, Short proofs of old results using spectral graph
theory, The Graham-Pollak Theorem, The Expander-Mixing Lemma, The
Hoffman-Singleton Theorem.
Author(s): Michael Tait, Carnegie Mellon University
This book describes
the following topics: The Derangements Problem, Binomial coefficients,
Principle of Inclusion and Exclusion, Rook Polynomials, Recurrences and
asymptotics, Convolutions and the Catalan Numbers, Exponential generating
functions, Ramsey Theory, Lovasz Local Lemma.
This PDF book
covers the following topics related to Combinatorics : What is Combinatorics,
Basic Counting Techniques, Permutations, Combinations, and the Binomial
Theorem, Bijections and Combinatorial Proofs, Counting with Repetitions,
Induction and Recursion, Generating Functions, Generating Functions and
Recursion, Some Important Recursively-Defined Sequences, Other Basic
Counting Techniques, Basics of Graph Theory, Moving through graphs,Euler and
Hamilton, Graph Colouring, Planar graphs, Latin squares, Designs, More
designs, Designs and Codes.
This PDF book
Combinatorics of Centers of 0-Hecke Algebrasin Type A covers the following
topics related to Combinatorics : Introduction, Preliminaries, Coxeter
groups, The symmetric group, Combinatorics, enters of 0-Hecke algebras,
Elements in stair form, Equivalence classes, etc.
This PDF covers the
following topics related to Combinatorics : Introduction, Enumeration,
Sequences and the Multiplication Principle, Permutations and Combinations,
Bijections and Double Counting, Estimation, Inclusion-Exclusion, Generating
Functions, Formal Power Series, Generating Functions Redux, Change making,
Compositions, Counting Subsets, Counting Strings, The Probabilistic Method,
Preliminaries, The first moment method, Linearity of expectation,
Alterations, Markov and Chebyshev, Chernoff Bound, Lov´asz Local Lemma,
Extremal Graph Theory, Tur´an’s Theorem, Projective planes, Sidon sets,
Constructing C4-free graphs, Ramsey numbers, Combinatorial Number Theory,
Erd os-Ko-Rado Theorem, Spectral graph theory, Linear Algebra Preliminaries,
The adjacency matrix, Short proofs of old results using spectral graph
theory, The Graham-Pollak Theorem, The Expander-Mixing Lemma, The
Hoffman-Singleton Theorem.
Author(s): Michael Tait, Carnegie Mellon University
Combinatotics is about counting without really counting
all possible cases one by one. This PDF covers the following topics related
to Combinatorics : Introduction, The Pigeonhole Principle, The Principle of
Extremals, The Principle of Invariants, Permutations and Combinations,
Combinations with Repetition, Inclusion–Exclusion principle, Recurrence
Relations, Generating Functions, Partitions of Natural Numbers.
Author(s): Stefanos Aretakis, University of
Toronto, Scarborough
The contents
of this book include: Basic Counting, Counting with Signs, Counting with
Ordinary Generating Functions, Counting with Exponential Generating
Functions, Counting with Partially Ordered Sets, Counting with Group
Actions, Counting with Symmetric Functions, Counting with Quasisymmetric
Functions, Introduction to Representation Theory.
The contents
of this book include: Selections and arrangements, Power series, Recurrence
relations, Partitions and permutations, The Principle of Inclusion and
Exclusion, Families of sets, Systems of distinct representatives, Latin
squares, Steiner triple systems.
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.
The purpose
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
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.