Enumerative CombinatoricsCRC Press, 29 maj 2002 - 632 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. |
Spis treści
BASIC COUNTING PRINCIPLES | 1 |
PERMUTATIONS AND COMBINATIONS | 39 |
FACTORIALS BINOMIAL AND MULTINOMIAL | 103 |
THE PRINCIPLE OF INCLUSION AND EXCLUSION | 131 |
PERMUTATIONS WITH FIXED POINTS AND SUCCES | 169 |
GENERATING FUNCTIONS | 191 |
STIRLING NUMBERS | 202 |
RECURRENCE RELATIONS | 233 |
PARTITION POLYNOMIALS | 411 |
CYCLES OF PERMUTATIONS | 461 |
EQUIVALENCE CLASSES | 487 |
RUNS OF PERMUTATIONS AND EULERIAN NUM | 513 |
HINTS AND ANSWERS TO EXERCISES | 545 |
| 591 | |
| 601 | |
| 609 | |
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A₁ Bell partition polynomials binomial coefficients binomial formula bivariate generating function Cartesian product circular permutations Cn,k combinatorial Consider the set COROLLARY corresponds cycle indicator cyclic group decomposed deduce the required distinguishable urns enumeration equals the number Eulerian numbers Example exclusion principle exponential generating function factorial moment Ferrers diagram Find the number finite set Wn group Gn group of permutations inclusion and exclusion indistinguishable balls initial conditions j-th k-permutations k₁ lattice paths models of coloring Multiplying Newton's binomial formula non-central nonnegative integer solutions Note number of different number of distributions number of k-combinations number of partitions number of permutations number p(n Pascal's triangle positive integer PROOF real number recurrence relation repetition required expression required number required recurrence relation resulting expression second kind sequence Show subsets summation is extended symmetric group Touchard polynomial triangular recurrence relation w₁ ΣΣ