Combinatorics Through Guided Discovery, 2004a

202 Index
pair structure, 159
pair,ordered, 3
partial fractions
method of, 88
partition
blocks of, 6
of a set, 5, 58
Stirling Numbers, 58
partition (of a set), 141
partition of a set
type vector, 59
partition of an integer, 63
conjugate of, 65
decreasing list, 64
Ferrers diagram, 64
into n parts, 63
self conjugate, 65
type vector, 64
Young diagram, 64
partitions of a set
number of, 59
Pascal’s Triangle, 12
path
in graph, 43
lattice, 20
diagonal, 20
length of, 48
permutation
k-element, 8
as a bijection, 11
broken, 57
cycle of, 112
two row notation, 107
permutation group, 105
picture enumerator, 74
picture enumerators
product principle for, 75
pigeonhole principle, 25
generalized, 26
Pólya-Redfield Theorem, 129
principle
bijection, 11
product, 5, 6
general, 6
quotient, 143
sum, 5, 6
principle of inclusion and exclusion,
93
for unions of sets, 95
principle of mathematical induction,
31, 147
probabilistic method, 36
product
Cartesian, 5
product notation, 8
product principle, 5, 6
for multisets, 122
general, 6, 34
picture enumerators, 75
product principle for exponential
generating functions, 160
product principle for generating
functions, 79
progression
arithmetic, 39
geometric, 40
proper coloring of a graph, 98
quotient principle, 18, 143
for multisets, 122
range (of a function), 133
recurrence, 38
constant coefficient, 86, 87
deletion-contraction, 48
linear, 40, 86, 87
linear homogeneous, 40
second order, 86, 87
solution to, 38
two variable, 58
recurrence relation, 38
recursive definition, 33
reflexive, 139
relation, 133
equivalence, 140, 142
of a function, 133
recurrence, 38
reflexive, 139, 140
transitive, 140
rising factorial power, 55
rotation group, 105
second order recurrence, 86
self-conjugate partition, 65