Combinatorics Through Guided Discovery, 2004a

200 Index
equivalent, 112
cycle index, 129
cycle monomial, 129
cyclic group, 113
definition
inductive, 33
recursive, 33
degree of a vertex, 42
degree sequence, 50, 72
ordered, 50
deletion, 47
deletion-contraction recurrence, 48,
99
derangement, 95
derangement problem, 95
diagram
of a partition
Ferrers, 64
Young, 64
digraph, 9, 135
dihedral group, 107
Dijkstra’s algorithm, 48
directed graph, 9, 135
disjoint, 4
multisets, 121
distance in a graph, 48
distance in a weighted graph, 48
domain (of a function), 133
double induction, 35
strong, 35
driving function, 40
Dyck path, 22
edge, 26, 41, 135
in a digraph, 135
of a complete graph, 26
EGF, 152
enumerator
fixed point, 127
orbit, 126
equivalence class, 141
equivalence relation, 140, 142
equivalent cycle, 112
exponential formula, 163
connected structures for, 165
exponential generating function, 152
exponential generating functions
product principle for, 160
exponential generating functions for
connected structures, 163
extended binomial theorem, 80
F-structures, 158
factorial, 8, 33, 55
q-ary, 84
falling, 55
factorial power
falling, 8
rising, 55
falling factorial power, 8, 55
Ferrers diagram, 64
Fibonacci numbers, 86, 88
fix, 121
fixed point enumerator, 127
function, 3, 133
alternate definition, 55
bijection, 11
characteristic, 14
composition, 137
digraph of, 9
driving, 40
identity, 104
injection, 4
inverse, 105
one-to-one, 4, 134
onto, 10, 134
and Stirling Numbers, 60
ordered, 55
onto, 55
relation of, 133
surjection, 10, 134
functions
composition of, 104
number of, 53
one-to-one
number of, 53
onto
number of, 97
general product principle, 6, 34
generating function, 76
exponential, 152
product principle for, 160
ordinary, 152
product principle for, 79