Combinatorics 8W940ZPW4E

URI	`m2://res/8W940ZPW4E`
Kind	course
Creators	Narayanan N (instructor)
Date	2022-10-11
Scope	in
Ids	course 03v0r5n49:111106155

Expressions

e1: edition

Language	en
Date	2022-10-11

m1: page, IIT Madras (record). nptel 111106155
m2: page, 2022-10-11 (record). nptel 111106155

Contents

part 1: Week 1
session 1: Pigeonhole Principle
session 2: Dirichlet theorem and Erdos-Szekeres Theorem
session 3: Ramey theorem as generalisation of PHP
session 4: An infinite flock of Pigeons
part 2: Week 2
session 5: Basic Counting - the sum and product rules
session 6: Examples of basic counting
session 7: Examples: Product and Division rules
session 8: Binomial theorem and bijective counting
session 9: Counting lattice paths
part 3: Week 3
session 10: Multinomial theorem
session 11: Applying Multinomial theorem
session 12: Integer compositions
session 13: Set partitions and Stirling numbers
session 14: Stirling and Hemachandra recursions
session 15: Integer partitions
part 4: Week 4
session 16: Young's diagram and Integer partitions
session 17: Principle of Inclusion and Exclusion
session 18: Applications of PIE
session 19: The twelvefold way
session 20: Inclusion exclusion: Linear algebra view
session 21: Partial Orders
part 5: Week 5
session 22: Mobius Inversion Formula
session 23: Product theorem and applications of Mobius Inversion
session 24: Formal power series, ordinary generating functions
session 25: Application of Ordinary generating functions
session 26: Product of Generating functions
part 6: Week 6
session 27: Composition of generating functions
session 28: Exponential Generating Function
session 29: Composition of EGF
session 30: Euler pentagonal number theorem
part 7: Week 7
session 31: Graphs - introduction
session 32: Paths Walks, Cycles
session 33: Digraphs and functional digraphs
session 34: Componenets, Connectivity, Bipartite graphs
part 8: Week 8
session 35: Acyclic graphs
session 36: Graph colouring
session 37: Mycielski graphs
session 38: Product of graphs
session 39: Menger's theorem
part 9: Week 9
session 40: System of Distinct representatives
session 41: Planar graphs
session 42: Euler identity
session 43: Map colouring problem - history
part 10: Week 10
session 44: The Discharging Method - part 1
session 45: The Discharging Method - part 2
session 46: Introduction to Group actions
session 47: Colouring and symmetries - examples
session 48: Burnside's lemma
part 11: Week 11
session 49: Proof of Burnsides lemma
session 50: Polya's theorem
session 51: Species of structures- definitions and examples
session 52: Associated seris and Product of species
session 53: Species: Substitution and Derivative
part 12: Week 12
session 54: Species: Pointing and countilg labelled trees
session 55: Review and Further directions
session 56: More on further topics
session 57: Linear Algebra method: Ultra short introduction
session 58: Probabiistic Method: Ultra short introduction

Catalogue records

nptel: 111106155 (manifestation)
nptel_video: 111106155 (manifestation)