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 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.
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
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.
The purpose
of this note is to give students a broad exposure to combinatorial mathematics,
using applications to emphasize fundamental concepts and techniques. Topics
covered includes: Introduction to Combinatorics, Strings, Sets, and Binomial
Coefficients, Induction, Combinatorial Basics, Graph Theory, Partially Ordered
Sets, Generating Functions, Recurrence Equations , Probability, Applying
Probability to Combinatorics, Combinatorial Applications of Network Flows,
Polya’s Enumeration Theorem.
Author(s): Mitchel T. Keller and William T. Trotter
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.