Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
Combinatorics by Michael Tait
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
103 Pages 
An Introduction to Algebraic Combinatorics by Darij Grinberg
This note describes the following topics: generating functions, Integer partitions and q binomial coefficients, Permutations, Alternating sums, signed counting and determinants.
Author(s): Darij Grinberg
692 Pages
Introduction to Combinatorics by Mark Wildon
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.
Author(s): Mark Wildon
146 Pages
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.
Author(s): Joy Morris, University of Lethbridge
357 Pages
Combinatorics of Centers by Sebastian Konig
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.
Author(s): Sebastian Konig
59 Pages
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
103 Pages
Introduction to Combinatorics by UToronto
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
63 Pages
Combinatorics The Art of Counting, Bruce E. Sagan
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.
Author(s): Bruce E. Sagan
325 Pages
Algebraic Combinatorics Lecture Notes
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.
Author(s): Sara Billey, Josh Swanson
101 Pages