《組合數(shù)學(xué)（英文版）（第5版）》英文影印版由Pearson Education Asia Ltd，授權(quán)機械工業(yè)出版社獨家出版。未經(jīng)出版者書面許可，不得以任何方式復(fù)制或抄襲奉巾內(nèi)容。僅限于中華人民共和國境內(nèi)（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。《組合數(shù)學(xué)（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(xué)麥迪遜分校數(shù)學(xué)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(xué)、圖論、線性代數(shù)和矩陣理論、編碼理論等。Brualdi教授的學(xué)術(shù)活動非常豐富。擔(dān)任過多種學(xué)術(shù)期刊的主編。2000年由于“在組合數(shù)學(xué)研究中所做出的杰出終身成就”而獲得組合數(shù)學(xué)及其應(yīng)用學(xué)會頒發(fā)的歐拉獎?wù)隆?/div>
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
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