Partitions and Permutations
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1 Chapter 5 Partitions and Permutations 5.1 Stirling Subset Numbers 5.2 Stirling Cycle Numbers 5.3 Inversions and Ascents 5.4 Derangements 5.5 Exponential Generating Functions 5.6 Posets and Lattices 1
2 2 Chapter 5 Partitions and Permutations
3 Section 5.1 Stirling Subset Numbers STIRLING SUBSET NUMBERS Non-Distinctness of Cells of a Partition
4 4 Chapter 5 Partitions and Permutations
5 Section 5.1 Stirling Subset Numbers 5
6 6 Chapter 5 Partitions and Permutations Every Cell of a Partition is Non-Empty
7 Section 5.1 Stirling Subset Numbers 7 Distinctness of Objects
8 8 Chapter 5 Partitions and Permutations The Type of a Partition
9 Section 5.1 Stirling Subset Numbers 9 Stirling s Subset Number Recurrence
10 10 Chapter 5 Partitions and Permutations Stirling s Triangle for Subset Numbers Table 5.1.1
11 Section 5.1 Stirling Subset Numbers 11 Rows Are Log-Concave Fig 5.1.1
12 12 Chapter 5 Partitions and Permutations
13 Section 5.1 Stirling Subset Numbers 13 Bell Numbers
14 14 Chapter 5 Partitions and Permutations
15 Section 5.1 Stirling Subset Numbers 15
16 16 Chapter 5 Partitions and Permutations Column-Sum Formulas
17 Section 5.1 Stirling Subset Numbers 17
18 18 Chapter 5 Partitions and Permutations
19 Section 5.1 Stirling Subset Numbers 19 Southeast Diagonal Sum
20 20 Chapter 5 Partitions and Permutations Stirling Numbers of the Second Kind
21 Section 5.1 Stirling Subset Numbers 21
22 22 Chapter 5 Partitions and Permutations
23 Section 5.1 Stirling Subset Numbers 23 Table 5.1.2
24 24 Chapter 5 Partitions and Permutations
25 Section 5.2 Stirling Cycle Numbers STIRLING CYCLE NUMBERS
26 26 Chapter 5 Partitions and Permutations
27 Section 5.2 Stirling Cycle Numbers 27 Non-Distinctness of the Cycles Stirling s Cycle Number Recurrence
28 28 Chapter 5 Partitions and Permutations Stirling s Triangle for Cycle Numbers
29 Section 5.2 Stirling Cycle Numbers 29 Table 5.2.1
30 30 Chapter 5 Partitions and Permutations
31 Section 5.2 Stirling Cycle Numbers 31 Rows are Log-Concave
32 32 Chapter 5 Partitions and Permutations
33 Section 5.2 Stirling Cycle Numbers 33 Fig Row Sums
34 34 Chapter 5 Partitions and Permutations
35 Section 5.2 Stirling Cycle Numbers 35
36 36 Chapter 5 Partitions and Permutations
37 Section 5.2 Stirling Cycle Numbers 37
38 38 Chapter 5 Partitions and Permutations
39 Section 5.2 Stirling Cycle Numbers 39 Columns
40 40 Chapter 5 Partitions and Permutations
41 Section 5.2 Stirling Cycle Numbers 41 Southeast Diagonal
42 42 Chapter 5 Partitions and Permutations Stirling Numbers of the First Kind
43 Section 5.2 Stirling Cycle Numbers 43
44 44 Chapter 5 Partitions and Permutations
45 Section 5.2 Stirling Cycle Numbers 45 Table 5.2.2
46 46 Chapter 5 Partitions and Permutations
47 Section 5.3 Inversions and Ascents INVERSIONS AND ASCENTS Inversions
48 48 Chapter 5 Partitions and Permutations
49 Section 5.3 Inversions and Ascents 49 Table 5.3.1
50 50 Chapter 5 Partitions and Permutations
51 Section 5.3 Inversions and Ascents 51
52 52 Chapter 5 Partitions and Permutations Ascents
53 Section 5.3 Inversions and Ascents 53 Eulerian Numbers
54 54 Chapter 5 Partitions and Permutations Table 5.3.2
55 Section 5.3 Inversions and Ascents 55
56 56 Chapter 5 Partitions and Permutations 5.4 DERANGEMENTS
57 Section 5.4 Derangements 57 Table 5.4.1
58 58 Chapter 5 Partitions and Permutations
59 Section 5.4 Derangements 59
60 60 Chapter 5 Partitions and Permutations 5.5 EXPONENTIAL GEN FUNCTIONS
61 Section 5.5 Exponential Gen Functions 61
62 62 Chapter 5 Partitions and Permutations
63 Section 5.5 Exponential Gen Functions 63 Counting Ordered Selections
64 64 Chapter 5 Partitions and Permutations
65 Section 5.5 Exponential Gen Functions 65
66 66 Chapter 5 Partitions and Permutations Counting Certain Kinds of Strings
67 Section 5.5 Exponential Gen Functions 67
68 68 Chapter 5 Partitions and Permutations
69 Section 5.5 Exponential Gen Functions 69
70 70 Chapter 5 Partitions and Permutations An Application To Stirling Subset #s
71 Section 5.5 Exponential Gen Functions 71
72 72 Chapter 5 Partitions and Permutations An EGF for Derangement Numbers
73 Section 5.5 Exponential Gen Functions 73
74 74 Chapter 5 Partitions and Permutations
75 Section 5.5 Exponential Gen Functions 75
76 76 Chapter 5 Partitions and Permutations 5.6 POSETS AND LATTICES
77 Section 5.6 Posets and Lattices 77 Products of Sets Cover Digraph
78 78 Chapter 5 Partitions and Permutations Fig The Boolean Poset
79 Section 5.6 Posets and Lattices 79 Fig The Divisibility Poset
80 80 Chapter 5 Partitions and Permutations Fig The Partition Poset
81 Section 5.6 Posets and Lattices 81 Fig 5.6.4
82 82 Chapter 5 Partitions and Permutations Inversion-Dominance Ordering on Perms
83 Section 5.6 Posets and Lattices 83 Fig 5.6.5
84 84 Chapter 5 Partitions and Permutations Minimal and Maximal Elements Fig 5.6.6
85 Section 5.6 Posets and Lattices 85 Lattice Property
86 86 Chapter 5 Partitions and Permutations
87 Section 5.6 Posets and Lattices 87 Fig 5.6.7
88 88 Chapter 5 Partitions and Permutations Fig Poset Isomorphism
89 Section 5.6 Posets and Lattices 89 Fig 5.6.9
90 90 Chapter 5 Partitions and Permutations Fig Chains and Antichains
91 Section 5.6 Posets and Lattices 91
92 92 Chapter 5 Partitions and Permutations
93 Section 5.6 Posets and Lattices 93 Fig
94 94 Chapter 5 Partitions and Permutations Ranked Posets
95 Section 5.6 Posets and Lattices 95 Fig
96 96 Chapter 5 Partitions and Permutations Linear Extensions
97 Section 5.6 Posets and Lattices 97 Algorithm 5.6.1:
98 98 Chapter 5 Partitions and Permutations Dilworth s Theorem
99 Section 5.6 Posets and Lattices 99
100 100 Chapter 5 Partitions and Permutations
101 Section 5.6 Posets and Lattices 101 Fig
102 102 Chapter 5 Partitions and Permutations
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