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 note describes
Elementary enumeration principles, Properties of binomial coefficients,
combinatorial identities, The principle of inclusion and exclusion,
Enumeration by means of recursions, The pigeon hole principle, Potential
functions and invariants, Some concepts in graph theory and various.
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 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
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.
This book
explains the following topics: Diagram Algebras and Hopf Algebras, Group
Representations, Sn-Representations Intro, Decomposition and Specht
Modules, Fundamental Specht Module Properties and Branching Rules,
Representation Ring for Sn and its Pieri Formula, Pieri for Schurs, Kostka
Numbers, Dual Bases, Cauchy Identity, Finishing Cauchy, Littlewood-Richardson
Rule, Frobenius Characteristic Map, Algebras and Coalgebras, Skew Schur
Functions and Comultiplication, Sweedler Notation, k-Coalgebra Homomorphisms,
Subcoalgebras, Coideals, Bialgebras, Bialgebra Examples, Hopf Algebras Defined,
Properties of Antipodes and Takeuchi’s Formula, etc.
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.