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
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.
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.
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 book covers the following topics: Fibonacci Numbers From a
Cominatorial Perspective, Functions,Sequences,Words,and Distributions, Subsets
with Prescribed Cardinality, Sequences of Two Sorts of Things with Prescribed
Frequency, Sequences of Integers with Prescribed Sum, Combinatorics and
Probability, Binary Relations, Factorial Polynomials, The Calculus of Finite
Differences, Principle of Inclusion and Exclusions.
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.