Expert steering Committee

Translator's order

order

Chapter 65438 +0 What is combinatorial mathematics?

1. 1 Example: Perfect chessboard coverage

1.2 Example: Cutting Cube

1.3 cases: magic prescription

1.4 case: four-color problem

1.5 case: 36 officer problem

1.6 Example: Shortest Path Problem

1.7 Example: nim sub-game.

1.8 movement

The second chapter pigeon coop principle

2. 1 pigeon nest principle: simple form

2.2 pigeon nest principle: enhanced form

2.3 Ramsey Theorem

2.4 practice

Chapter III Arrangement and Combination

3. 1 Four Basic Counting Principles

.3.2 Arrangement of units

3.3 Combination of sets

3.4 Arrangement of multiset

3.5 multiset's combination

3.6 practice

Chapter 4 Generating permutation and combination

4. 1 generate permutation

4.2 The arrangement order is opposite

4.3 Generate combinations

4.4 generate divination combination

4.5 Partial Order and Equivalence Relation

4.6 practice

The fifth chapter binomial coefficient

5. 1 Pascal formula

5.2 binomial theorem

5.3 Some identities

5.4 Unimodal property of binomial coefficient

5.5 multinomial theorem

5.6 Newton binomial theorem

5.7 Re-discussion on posets

5.8 practice

Chapter VI Exclusion Principle and Application

6. 1 incompatibility principle

6.2 Repeated combination

6.3 dislocation arrangement

6.4 arrangement of prohibited positions

6.5 No discharge position in the second phase

6.6 Mobius inversion

6.7 practice

Chapter 7 Recursive Relation and Generating Function

7. 1 some sequences

7.2 Linear homogeneous recurrence relation

7.3 Non-homogeneous recursive relation

7.4 Generating function

7.5 Recursive and Generative Functions

7.6 An example of geometry

7.7 Exponential Generation Function

7.8 practice

Chapter 8 Special Counting Sequence

8. 1 Catalan number

8.2 Difference Sequence and Stirling Number

8.3 partition number

8.4 a geometry problem

8.5 Lattice Path and Schroeder Number

8.6 practice

Chapter 9 Matching in Bipartite Graphs

9. 1 general problem expression

9.2 Matching

9.3 Different Representation Systems

9.4 A stable marriage

9.5 practice

Chapter 10 Combination Design

10. 1 modular operation

Block design of 10.2

10.3 Steiner ternary

10.4 Latin square

10.5 exercise

Chapter 1 1 Graph Theory Guidance

The basic properties of 1 1. 1

1 1.2 Euler trace

1 1.3 Hamilton Road and Hamilton Circle

1 1.4 bipartite multigraph

1 1.5 tree

1 1.6 Shannon switch game

1 1.7 Re-discussion on Tree

1 1.8 motion

12 chapter directed graph and network

12. 1 directed graph

12.2 network

12.3 exercise

Chapter 13 Re-discussion on figure

13. 1 chromatic number

13.2 plan and plan

13.3 five-color theorem

13.4 Independent number and group number

13.5 connection

13.6 exercise

Chapter 14 Paulia counting method

Permutation groups and symmetric groups of 14. 1

14.2 burnside theorem

14.3 Paulia counting formula

14.4 exercise

Answers and tips for exercises

refer to

index