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.

This note
describes the following topics: generating functions, Integer partitions and q binomial coefficients,
Permutations, Alternating sums, signed counting and determinants.

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 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.

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.

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.

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.