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.
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.
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.
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.