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Introduction to combinatorial theory

Introduction to combinatorial theory

Material type
단행본
Personal Author
Bose, R. C. (Raj Chandra), 1901- Manvel, B. (Bennet), 1943-
Title Statement
Introduction to combinatorial theory / R.C. Bose and B. Manvel.
Publication, Distribution, etc
New York :   Wiley,   c1984.  
Physical Medium
ix, 237 p. : ill. ; 24 cm.
Series Statement
Wiley series in probability and mathematical statistics.Probability and mathematical statistics, 0271-6232
ISBN
0471896144 :
Bibliography, Etc. Note
Includes bibliographical references and index.
Subject Added Entry-Topical Term
Combinatorial analysis.
000 00818camuuu200229 a 4500
001 000000072811
005 .0
008 830801s1984 nyua b 00110 eng
010 ▼a 83017019 //r84
020 ▼a 0471896144 : ▼c $24.95 (est.)
049 ▼a l412616764
050 0 ▼a QA164 ▼b .B67 1984
082 0 ▼a 511/.6 ▼2 19
090 ▼a 512.5 ▼b B743i
100 1 0 ▼a Bose, R. C. ▼q (Raj Chandra), ▼d 1901-
245 1 0 ▼a Introduction to combinatorial theory / ▼c R.C. Bose and B. Manvel.
260 0 ▼a New York : ▼b Wiley, ▼c c1984.
300 ▼a ix, 237 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a Wiley series in probability and mathematical statistics. ▼p Probability and mathematical statistics, ▼x 0271-6232
504 ▼a Includes bibliographical references and index.
650 0 ▼a Combinatorial analysis.
700 1 0 ▼a Manvel, B. ▼q (Bennet), ▼d 1943-

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.5 B743i Accession No. 412616764 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

CONTENTS
1. Permutations and Combinations = 1
  1.1. Two Counting Principles = 1
  1.2. Ordered Choices = 4
  1.3. Unordered Choices = 7
  1.4. Circular and Restricted Arrangements = 11
  1.5. Finite Probability = 14
  1.6. Compound Events and Expectations = 18
  1.7. Remarks = 23
2. The Binomial Theorem = 24
  2.1. The Binomial Theorem = 24
  2.2. Binomial Identities = 27
  2.3. Multinomial Coefficients and Negative Binomial Coefficients = 33
  2.4. Binomial Probabilities = 38
  2.5. Remarks = 42
3. Enumeration = 44
  3.1. Fibonacci Numbers = 44
  3.2. Linear Diophantine Equations = 47
  3.3. Inclusion - Exclusion = 50
  3.4. Partitions = 55
  3.5. Generating Functions = 57
  3.6. Recurrence Relations = 62
  3.7. Remarks = 69
4. Graphs = 70
  4.1. Introduction = 70
  4.2. Basic Concepts = 73
  4.3. Eulerian Trails = 77
  4.4. Hamiltonian Graphs = 81
  4.5. Trees = 87
  4.6. Binary Trees = 91
  4.7. Remarks = 98
5. Finite Fields = 99
  5.1. Introduction = 99
  5.2. The Galois Field, G FP = 102
  5.3. The Commutative Ring G FP [x] = 105
  5.4. The Galois Field G F Pn = 108
  5.5. Primitive Elements of G F Pn = 111
  5.6. Operation in G F Pn = 113
  5.7. Remarks = 118
6. Finite Plane Geometries = 119
  6.1. The Geometry EG(2, Pn ) = 119
  6.2. Some Properties of the Geometry EG(2, Pn ) = 124
  6.3. The Projective Geometry PG(2, Pn ) = 130
  6.4. Remarks = 134
7. Orthogonal Latin Squares and Error Correcting Codes = 135
  7.1. Latin Squares = 135
  7.2. Complete Sets of Orthogonal Latin Squares = 139
  7.3. Error - Correcting Codes = 144
  7.4. Hamming One - Error Correcting Binary Codes = 149
  7.5. Remarks = 153
8. Balanced Incomplete Block Designs = 155
  8.1. Relations Between Parameters = 155
  8.2. Incidence Matrix of a BIB Design = 158
  8.3. Symmetric BIB Designs = 163
  8.4. Orthogonal Series Designs = 167
  8.5. Symmetrically Repeated Differences = 170
  8.6. Steiner Triples = 174
  8.7. Symmetric BIB Designs with r = (v - 1)/2 = 177
  8.8. The Residual and Derived of a Symmetric BIB Design = 179
  8.9. Remarks = 182
9. Problems of Choice = 184
  9.1. Introduction = 184
  9.2. The Pigeonhole Principle = 185
  9.3. Ramsey's Theorem = 187
  9.4. Erd o ·· s and Szekeres' Theorem = 192
  9.5. Parity = 195
  9.6. Remarks = 200
10. Optimization = 202
  10.1. Introduction = 202
  10.2. The Marriage Theorem = 205
  10.3. Applications = 211
  10.4. Algorithms for Matchings = 216
  10.5. Maximum Flows = 220
  10.6. Remarks = 231
Index = 233

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