組合學 (第二版) (英文) (美)尼古拉斯.A洛爾 9787576706215 【台灣高等教育出版社】

目錄 Preface to the Second Edition
Introduction
I Counting
1 Basic Counting
1 1 The Product Rule
1 2 The Sum Rule
1 3 Counting Words and Permutations
1 4 Counting Subsets
1 5 Counting Anagrams
1 6 Counting Rules for Set Operations
1 7 Probability
1 8 Lotteries and Card Games
1 9 Conditional Probability and Independence
1 10 Counting Functions
1 11 Cardinality and the Bijection Rule
1 12 Counting Multisets and Compositions
1 13 Counting Balls in Boxes
1 14 Counting Lattice Paths
1 15 Proofs of the Sum Rule and the Product Rule
Summary
Exercises
2 Combinatorial Identities and Recursions
2 1 Initial Examples of Combinatorial Proofs
2 2 The Geometric Series Formula
2 3 The Binomial Theorem
2 4 The Multinomial Theorem
2 5 More Binomial Coefficient Identities
2 6 Sums of Powers of Integers
2 7 Recursions
2 8 Recursions for Multisets and Anagrams
2 9 Recursions for Lattice Paths
2 10 Catalan Recursions
2 11 Integer Partitions
2 12 Set Partitions
2 13 Surjections， Balls in Boxes， and Equivalence Relations
2 14 Stirling Numbers and Rook Theory
2 15 Stirling Numbers and Polynomials
2 16 Solving Recursions with Constant Coefficients
Summary
Exercises
3 Counting Problems in Graph Theory
3 1 Graphs and Digraphs
3 2 Walks and Matrices
3 3 Directed Acyclic Graphs and Nilpotent Matrices
3 4 Vertex Degrees
3 5 Functional Digraphs
3 6 Cycle Structure of Permutations
3 7 Counting Rooted Trees
3 8 Connectedness and Components
3 9 Forests
3 10 Trees
3 11 Counting Trees
3 12 Pruning Maps
3 13 Bipartite Graphs
3 14 Matchings and Vertex Covers
3 15 Two Matching Theorems
3 16 Graph Coloring
3 17 Spanning Trees
3 18 The Matrix-Tree Theorem
3 19 Eulerian Tours
Summary
Exercises
4 Inclusion-Exclusion， Involutions， and M6bius Inversion
4 1 The Inclusion-Exclusion Formula
4 2 Examples of the Inclusion-Exclusion Formula
4 3 Surjections and Stirling Numbers
4 4 Euler's φ Function
4 5 Derangements
4 6 Involutions
4 7 Involutions Related to Inclusion-Exclusion
4 8 Generalized Inclusion-Exclusion Formulas
4 9 MSbius Inversion in Number Theory
4 10 Partially Ordered Sets
4 11 M6bius Inversion for Posets
4 12 Product Posers
Summary
Exercises
5 Generating Functions
5 1 What is a Generating Function?
5 2 Convergence of Power Series
5 3 Examples of Analytic Power Series
5 4 Operations on Power Series
5 5 Solving Recursions with Generating Functions
5 6 Evaluating Summations with Generating Functions
5 7 Generating Function for Derangements
5 8 Counting Rules for Weighted Sets
5 9 Examples Of the Product Rule for Weighted Sets
5 10 Generating Functions for Trees
5 11 Tree Bijections
5 12 Exponential Generating Functions
5 13 Stirling Numbers of the First Kind
5 14 Stirling Numbers of the Second Kind
5 15 Generating Functions for Integer Partitions
5 16 Partition Bijections
5 17 Euler's Pentagonal Number Theorem
Summary
Exercises
6 Ranking， Unranking， and Successor Algorithms
6 1 Introduction to Ranking and Successor Algorithms
6 2 The Bijective Sum Rule
6 3 The Bijective Product Rule for Two Sets
6 4 The Bijective Product Rule
6 5 Ranking Words
6 6 Ranking Permutations
6 7 Ranking Subsets
6 8 Ranking Anagrams
6 9 Ranking Integer Partitions
6 10 Ranking Set Partitions
6 11 Ranking Trees
6 12 The Successor Sum Rule
6 13 Successor Algorithms for Anagrams
6 14 The Successor Product Rule
6 15 Successor Algorithms for Set Partitions
6 16 Suc
詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。