Enumerative combinatorics / Charalambos A. Charalambides.

Format:

Book

Author/Creator:

Charalambides, Ch. A.

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Discrete mathematics and its applications

Discrete mathematics and its applications.

Language:

English

Subjects (All):

Combinatorial enumeration problems.

Physical Description:

xvi, 609 pages : illustrations ; 24 cm.

Place of Publication:

Boca Raton, Fla. : Chapman & Hall/CRC, [2002]

Contents:

1 Basic Counting Principles 1

1.2 Sets, relations and maps 3

1.2.1 Basic notions 3

1.2.2 Cartesian product 5

1.2.3 Relations 7

1.2.5 Countable and uncountable sets 9

1.2.6 Set operations 9

1.2.7 Divisions and partitions of a set 13

1.3 The principles of addition and multiplication 14

1.4 Discrete probability 24

1.5 Sums and products 27

2 Permutations and Combinations 39

2.2 Permutations 40

2.3 Combinations 51

2.4 Divisions and partitions of a finite set 62

2.5 Integer solutions of a linear equation 68

2.6 Lattice paths 75

2.7 Probabilistic applications 82

2.7.1 Classical problems in discrete probability 82

2.7.2 Ordered and unordered samples 86

2.7.3 Probability models in statistical mechanics 89

3 Factorials, Binomial and Multinomial Coefficients 103

3.2 Factorials 104

3.3 Binomial coefficients 110

3.4 Multinomial coefficients 123

4 The Principle of Inclusion and Exclusion 131

4.2 Number of elements in a union of sets 132

4.3 Number of elements in a given number of sets 144

4.4 Bonferroni inequalities 152

4.5 Number of elements of a given rank 155

5 Permutations with Fixed Points and Successions 169

5.2 Permutations with fixed points 169

5.3 Ranks of permutations 174

5.4 Permutations with successions 176

5.5 Circular permutations with successions 180

6 Generating Functions 191

6.2 Univariate generating functions 192

6.2.1 Definitions and basic properties 192

6.2.2 Power, factorial and Lagrange series 202

6.3 Combinations and permutations 208

6.4 Moment generating functions 215

6.5 Multivariate generating functions 219

7 Recurrence Relations 233

7.2 Basic notions 233

7.3 Recurrence relations of the first order 235

7.4 The method of characteristic roots 239

7.5 The method of generating functions 250

8 Stirling Numbers 277

8.2 Stirling numbers of the first and second kind 278

8.3 Explicit expressions and recurrence relations 289

8.4 Generalized factorial coefficients 301

8.5 Non-central Stirling and related numbers 314

9 Distributions and Occupancy 339

9.2 Classical occupancy and modifications 340

9.3 Ordered distributions and occupancy 348

9.4 Balls of general specification and distinguishable urns 350

9.5 Generating functions 353

10 Partitions of Integers 369

10.2 Recurrence relations and generating functions 370

10.3 A universal generating function 376

10.4 Interrelations among partition numbers 383

10.5 Combinatorial identities 391

11 Partition Polynomials 411

11.2 Exponential Bell partition polynomials 412

11.3 General partition polynomials 419

11.4 Logarithmic partition polynomials 424

11.5 Potential partition polynomials 428

11.6 Inversion of power series 433

11.7 Touchard polynomials 442

12 Cycles of Permutations 461

12.2 Permutations with a given number of cycles 462

12.3 Even and odd permutations 468

12.4 Permutations with partially ordered cycles 471

13 Equivalence Classes 487

13.2 Cycle indicator of a permutation group 488

13.3 Orbits of elements of a finite set 493

13.4 Models of colorings of a finite set 499

14 Runs of Permutations and Eulerian Numbers 513

14.2 Eulerian numbers 513

14.3 Carlitz numbers 522

14.4 Permutations with a given number of runs 530

14.5 Permutations with repetition and a given number of runs 533.

Notes:

Includes bibliographical references (pages [591]-600) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

1584882905

OCLC:

48905738