組合數(shù)學（英文版第5版）

定　價：￥49.00

作　者：	（美）布魯?shù)?著
出版社：	機械工業(yè)出版社
叢編項：	經典原版書庫
標　簽：	組合理論

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ISBN：	9787111265252	出版時間：	2009-03-01	包裝：	平裝
開本：	32開	頁數(shù)：	605	字數(shù)：

內容簡介

　　《組合數(shù)學（英文版）（第5版）》英文影印版由Pearson Education Asia Ltd，授權機械工業(yè)出版社獨家出版。未經出版者書面許可，不得以任何方式復制或抄襲奉巾內容。僅限于中華人民共和國境內（不包括中國香港、澳門特別行政區(qū)和中同臺灣地區(qū)）銷售發(fā)行?！督M合數(shù)學（英文版）（第5版）》封面貼有Pearson Education（培生教育出版集團）激光防偽標簽，無標簽者不得銷售。English reprint edition copyright@2009 by Pearson Education Asia Limited and China Machine Press．Original English language title：Introductory Combinatorics，F(xiàn)ifth Edition（ISBN978—0—1 3-602040-0）by Richard A．Brualdi，Copyright@2010，2004，1999，1992，1977 by Pearson Education，lnc． All rights reserved．Published by arrangement with the original publisher，Pearson Education，Inc．publishing as Prentice Hall．For sale and distribution in the People’S Republic of China exclusively（except Taiwan，Hung Kong SAR and Macau SAR）．

作者簡介

　　Richard A.Brualdi，美國威斯康星大學麥迪遜分校數(shù)學系教授（現(xiàn)已退休）。曾任該系主任多年。他的研究方向包括組合數(shù)學、圖論、線性代數(shù)和矩陣理論、編碼理論等。Brualdi教授的學術活動非常豐富。擔任過多種學術期刊的主編。2000年由于“在組合數(shù)學研究中所做出的杰出終身成就”而獲得組合數(shù)學及其應用學會頒發(fā)的歐拉獎章。

圖書目錄

1 What Is Combinatorics?
1.1 Example：Perfect Covers of Chessboards
1.2 Example：Magic Squares
1.3 Example：The Fou r-CoIor Problem
1.4 Example：The Problem of the 36 C)fficers
1.5 Example：Shortest-Route Problem
1.6 Example：Mutually Overlapping Circles
1.7 Example：The Game of Nim
1.8 Exercises
2 Permutations and Combinations
2.1 Four Basic Counting Principles
2.2 Permutations of Sets
2.3 Combinations(Subsets)of Sets
2.4 Permutations ofMUltisets
2.5 Cornblnations of Multisets
2.6 Finite Probability
2.7 Exercises
3 The Pigeonhole Principle
3.1 Pigeonhole Principle：Simple Form
3.2 Pigeon hole Principle：Strong Form
3.3 A Theorem of Ramsey
3.4 Exercises
4 Generating Permutations and Cornbinations
4.1 Generating Permutations
4.2 Inversions in Permutations
4.3 Generating Combinations
4.4 Generating r-Subsets
4.5 PortiaI Orders and Equivalence Relations
4.6 Exercises
5 The Binomiaf Coefficients
5.1 Pascals Triangle
5.2 The BinomiaI Theorem
5.3 Ueimodality of BinomiaI Coefficients
5.4 The Multinomial Theorem
5.5 Newtons Binomial Theorem
5.6 More on Pa rtially Ordered Sets
5.7 Exercises
6 The Inclusion-Exclusion P rinciple and Applications
6.1 The In Clusion-ExclusiOn Principle
6.2 Combinations with Repetition
6.3 Derangements+
6.4 Permutations with Forbidden Positions
6.5 Another Forbidden Position Problem
6.6 M6bius lnverslon
6.7 Exe rcises
7 Recurrence Relations and Generating Functions
7.1 Some Number Sequences
7.2 Gene rating Functions
7.3 Exponential Generating Functions
7.4 Solving Linear Homogeneous Recurrence Relations
7.5 Nonhomogeneous Recurrence Relations
7.6 A Geometry Example
7.7 Exercises
8 Special Counting Sequences
8.1 Catalan Numbers
8.2 Difference Sequences and Sti rling Numbers
8.3 Partition Numbers
8.4 A Geometric Problem
8.5 Lattice Paths and Sch rSder Numbers
8.6 Exercises Systems of Distinct ReDresentatives
9.1 GeneraI Problem Formulation
9.2 Existence of SDRs
9.3 Stable Marriages
9.4 Exercises
10 CombinatoriaI Designs
10.1 Modular Arithmetic
10.2 Block Designs
10.3 SteinerTriple Systems
10.4 Latin Squares
10.5 Exercises
11 fntroduction to Graph Theory
11.1 Basic Properties
11.2 Eulerian Trails
11.3 Hamilton Paths and Cycles
11.4 Bipartite Multigraphs
11.5 Trees
11.6 The Shannon Switching Game
11.7 More on Trees
11.8 Exercises
12 More on Graph Theory
12.1 Chromatic Number
12.2 Plane and Planar Graphs
12.3 A Five-Color Theorem
12.4 Independence Number and Clique Number
12.5 Matching Number
12.6 Connectivity
12.7 Exercises
13 Digraphs and Networks
13.1 Digraphs
13.2 Networks
13.3 Matchings in Bipartite Graphs Revisited
13.4 Exercises
14 Polya Counting
14.1 Permutation and Symmetry Groups
14.2 Bu rnsides Theorem
14.3 Polas Counting Formula
14.4 Exercises
Answers and Hints to Exercises