Foundations of Combinatorics with Applications

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

Combinatorics Lecture Notes by Stephan Wagner

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.

Author(s): Stephan Wagner

69 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

Combinatorics by Joy Morris

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

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

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

Lecture Notes Combinatorics

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.

Author(s): Torsten Ueckerdt

137 Pages