Enumerative Combinatorics

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Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.show more

Product details

  • Hardback | 632 pages
  • 159.5 x 244.9 x 39.1mm | 1,025.13g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 14 black & white illustrations, 18 black & white tables, 1 black & white halftones
  • 1584882905
  • 9781584882909
  • 2,383,282

Review quote

"The broad field of applications of combinatorial methods makes this book useful to anyone interested in operations research, physical, or social sciences. Provides a comprehensive coverage of enumerative combinatorics, and gives many illuminating examples and interesting historical notes students of combinatorics will find the book very useful as there are many theorems, all with complete proofs, and many exercises with hints and answers." -Journal of the Operational Research Society, Vol 55, no. 2, 2004show more

Table of contents

BASIC COUNTING PRINCIPLES Introduction Sets, Relations and Maps The Principles of Addition and Multiplication Discrete Probability Sums and Products PERMUTATIONS AND COMBINATIONS Introduction Permutations Combinations Divisions and Partitions of a Finite set Integer Solutions of a Linear Equation Lattice Paths Probabilistic Applications FACTORIALS, BINOMIAL AND MULTINOMIAL COEFFICIENTS Introduction Factorials Binomial Coefficients Multinomial Coefficients THE PRINCIPLE OF INCLUSION AND EXCLUSION Introduction Number of Elements in a Union of Sets Number of Elements in a Given Number of Sets Bonferroni Inequalities Number of Elements of a Given Rank PERMUTATIONS WITH FIXED POINTS AND SUCCESSIONS Introduction Permutations with Fixed Points Ranks of Permutations Permutations with Successions Circular Permutations with Successions GENERATING FUNCTIONS Introduction Univariate Generating Functions Combinations and Permutations Moment Generating Functions Multivariate Generating Functions RECURRENCE RELATIONS Introduction Basic Notions Recurrence Relations of the First Order The Method of Characteristic Roots The Method of Generating Functions STIRLING NUMBERS Introduction Stirling Numbers of the First and Second Kind Explicit Expressions and Recurrence Relations Generalized Factorial Coefficients Non-Central Stirling and Related Numbers DISTRIBUTIONS AND OCCUPANCY Introduction Classical Occupancy and Modifications Ordered Distributions and Occupancy Balls of General Specification and Distinguishable Urns Generating Functions PARTITIONS OF INTEGERS Introduction Recurrence Relations and Generating Functions A Universal Generating Function Interrelations among Partition Numbers Combinatorial Identities PARTITION POLYNOMIALS Introduction Exponential Bell Partition Polynomials General Partition Polynomials Logarithmic Partition Polynomials Potential Partition Polynomials Inversion of Power Series Touchard Polynomials CYCLES OF PERMUTATIONS Introduction Permutations with a Given Number of Cycles Even and Odd Permutations Permutations with Partially Ordered Cycles EQUIVALENCE CLASSES Introduction Cycle Indicator of a Permutation Group Orbits of Elements of a Finite Set Models of Colorings of a Finite Set RUNS OF PERMUTATIONS AND EULERIAN NUMBERS Introduction Eulerian Numbers Carlitz Numbers Permutations with a Given Number of Runs Permutations with Repetition and a Given Number of Runs HINTS AND ANSWERS TO EXERCISES BIBLIOGRAPHY INDEX Each chapter also contains Bibliographic Notes and Exercisesshow more