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Index Index

\(\Pi\) notation, Paragraph
\(n"!\), Paragraph
Stirling's formula for, Problem
\(n^{\overline{k}}\), Paragraph
\(n^{\underline{k}}\), Paragraph
\(q\)-ary factorial, Problem
\(q\)-binomial coefficient, Problem
\(S(k,n)\), Paragraph Problem
action of a group on a set, Paragraph
arithmetic progression, Problem
arithmetic series, Problem
associative law, Problem
asymptotic combinatorics, Paragraph
automorphism (of a graph), Problem Problem
basis (for polynomials), Paragraph
Bell Number, Problem
bijection, Paragraph Paragraph
bijection principle, Paragraph
binomial coefficient, Paragraph
\(q\)-binomial, Problem
Binomial Theorem, Problem
extended, Problem
block of a partition, Paragraph Paragraph
broken permutation, Paragraph
Burnside's Lemma, Paragraph
Cartesian product, Paragraph
Catalan Number, Problem Problem Problem
generating function for, Problem
recurrence for, Problem Exercise
Catalan Path, Problem
Cauchy-Frobenius-Burnside Theorem, Paragraph
characteristic function, Problem
chromatic polynomial of a graph, Paragraph
Chung-Feller Theorem, Problem
closure property, Item
multinomial, Problem
standard notation, Paragraph
standard ordering, Paragraph
coloring of a graph, Paragraph
proper, Paragraph
combinations, Paragraph
commutative law, Paragraph
complement, Problem
complement of a partition, Problem
composition, Exercise Paragraph
\(k\) parts, Exercise
number of, Exercise
composition of functions, Problem
number of, Exercise
congruence modulo \(n\), Problem
conjugate of an integer partition, Problem
connected component graph, Problem
connected component of a graph, Paragraph Paragraph
connected structures and EGFs, Paragraph
constant coefficient linear recurrence, Paragraph
contraction, Paragraph
cost of a spanning tree, Paragraph
cycle (in a graph), Problem
cycle (of a permutation), Paragraph
element of, Paragraph
equivalent, Paragraph
cycle index, Problem
cycle monomial, Problem
cyclic group, Paragraph
inductive, Paragraph
recursive, Paragraph
degree of a vertex, Paragraph
degree sequence, Exercise Exercise
ordered, Exercise
deletion, Paragraph
deletion-contraction recurrence, Problem Problem
derangement, Paragraph
derangement problem, Paragraph
of a partition!Ferrers, Paragraph
of a partition!Young, Paragraph
dihedral group, Subsection
Dijkstra's algorithm, Problem
directed graph, Paragraph Paragraph
disjoint, Problem
multisets, Paragraph
distance in a graph, Problem
distance in a weighted graph, Paragraph
domain (of a function), Paragraph
double induction, Paragraph Quotation
strong, Paragraph
driving function, Paragraph
Dyck path, Problem
in a digraph, Paragraph
of a complete graph, Paragraph
EGF, Paragraph
encomplement of a partition, Problem
fixed point, Problem
orbit, Problem
equivalence class, Paragraph
equivalence relation, Paragraph Theorem
equivalent cycle, Paragraph
exponential formula, Paragraph
connected structures for, Paragraph
exponential generating function, Paragraph
exponential generating functions
product principle for, Paragraph
exponential generating functions for connected structures, Paragraph
extended binomial theorem, Problem
F-structures, Paragraph
\(q\)-ary, Problem
falling, Paragraph
factorial power
falling, Paragraph
rising, Paragraph
falling factorial power, Paragraph Paragraph
Ferrers diagram, Paragraph
Fibonacci numbers, Paragraph Problem
fix, Paragraph
fixed point enumerator, Problem
function, Problem Paragraph
alternate definition, Paragraph
bijection, Paragraph
characteristic, Problem
composition, Paragraph
digraph of, Paragraph
driving, Paragraph
identity, Paragraph
injection, Problem
inverse, Paragraph
one-to-one, Problem Problem
onto!and Stirling Numbers, Problem
ordered, Paragraph
ordered!onto, Paragraph
relation of, Paragraph
surjection, Problem Problem
composition of, Problem
number of, Theorem
one-to-one!number of, Theorem
onto!number of, Problem
general product principle, Paragraph Paragraph
generating function, Paragraph
exponential, Paragraph
exponential!product principle for, Paragraph
ordinary, Paragraph
product principle for, Problem
geometric progression, Paragraph
geometric series, Paragraph Problem
graph, Paragraph
chromatic polynomial of, Paragraph
coloring of, Paragraph
coloring of!proper, Paragraph
complete, Paragraph
connected component of, Paragraph Paragraph
coordinate, Paragraph
directed, Paragraph Paragraph
distance in, Paragraph
simple, Paragraph
isomorphic, Problem
Gray Code, Exercise
greedy method, Paragraph
group acting on a set, Paragraph
group action on colorings, Paragraph
group of permutations, Paragraph
hatcheck problem, Paragraph
homogeneous linear recurrence, Paragraph
identity function, Paragraph Paragraph
identity property, Item
identity property (for permutations), Paragraph
inclusion and exclusion principle, Paragraph
for unions of sets, Paragraph
indicator polynomials, Paragraph
mathematical, the principle of, Paragraph Quotation Paragraph
mathematical, the strong principle of, Quotation
strong double, Paragraph
conclusion, Paragraph
hypothesis, Paragraph
step, Paragraph
inductive definition, Paragraph
injection, Problem Problem
inverse function, Paragraph
inverse property, Item
involution, Problem
isometry, Problem
graphs, Problem
k-set structures, Paragraph
Lah number, Paragraph
lattice path, Problem
diagonal, Problem
length (of a path), Paragraph
linear recurrence, Paragraph Paragraph
constant coefficient, Paragraph
homogeneous, Paragraph
second order, Problem
mathematical induction
strong double, Paragraph
probabilistic, Paragraph
minimum cost spanning tree, Problem
monochromatic subgraph, Problem
multinomial coefficient, Problem
multiorbit, Paragraph
multiorbits, Problem
multiplicity in a multiset, Problem
multiset, Problem
product principle, Paragraph
quotient principle, Paragraph
sum principle, Quotation
union, Paragraph
ménage problem, Problem
one-to-one, Problem
one-to-one function, Problem
onto function, Problem Problem
counting, Problem
ordered, Paragraph
onto functions
number of, Problem
orbit, Paragraph
orbit enumerator, Problem
Orbit-Fixed Point Theorem, Problem Paragraph
ordered degree sequence, Exercise
ordered function, Paragraph
ordered onto function, Paragraph
ordered pair, Problem
ordinary generating function, Paragraph
pair structure, Paragraph
pair,ordered, Problem
partial fractions
method of, Paragraph
blocks of, Paragraph
of a set, Paragraph Paragraph
Stirling Numbers, Paragraph
partition (of a set), Paragraph
partition of a set
type vector, Problem
partition of an integer, Paragraph
conjugate of, Problem
decreasing list, Problem
Ferrers diagram, Paragraph
into \(n\) parts, Paragraph
self conjugate, Problem
type vector, Problem
Young diagram, Paragraph
partitions of a set
number of, Problem
Pascal's Triangle, Paragraph
in graph, Problem
lattice, Problem
lattice!diagonal, Problem
length of, Paragraph
\(k\)-element, Problem
as a bijection, Problem
broken, Paragraph
cycle of, Paragraph
two row notation, Paragraph
permutation group, Paragraph
picture enumerator, Paragraph
picture enumerators
product principle for, Problem
pigeonhole principle, Paragraph
generalized, Problem
bijection, Paragraph
product!general, Paragraph
quotient, Paragraph
principle of inclusion and exclusion, Paragraph
for unions of sets, Paragraph
principle of mathematical induction, Paragraph Quotation Paragraph
probabilistic method, Paragraph
Cartesian, Paragraph
product notation, Paragraph
product principle, Paragraph Paragraph
for multisets, Paragraph
picture enumerators, Problem
product principle for exponential generating functions, Paragraph
product principle for generating functions, Problem
arithmetic, Problem
geometric, Paragraph
proper coloring of a graph, Paragraph
Pólya-Redfield Theorem, Problem
quotient principle, Paragraph Paragraph
for multisets, Paragraph
range (of a function), Paragraph
recurrence, Paragraph
constant coefficient, Problem Paragraph
deletion-contraction, Problem
linear homogeneous, Paragraph
second order, Problem Paragraph
solution to, Paragraph
two variable, Paragraph
recurrence relation, Paragraph
recursive definition, Paragraph
reflexive, Item
relation, Paragraph
equivalence, Paragraph Theorem
of a function, Paragraph
recurrence, Paragraph
reflexive, Item Item
transitive, Item
rising factorial power, Paragraph
rotation group, Paragraph
second order recurrence, Problem
self-conjugate partition, Problem
degree, Exercise
arithmetic, Problem
geometric, Paragraph Problem
colorings of action of a group on, Subsection
disjoint, Problem
mutually disjoint, Problem
simple graph, Paragraph
space of polynomials, Paragraph
spanning tree, Paragraph
cost of, Paragraph
minimum cost, Problem
species, Paragraph
exponential generating function for, Paragraph
standard notation for a coloring, Paragraph
Stirling Number
first kind, Problem
second kind, Paragraph Problem
Stirling's formula for \(n"!\), Problem
Stirling's triangle
first kind, Problem
second kind, Problem
strong double induction, Paragraph
strong principle of mathematical induction, Quotation
structure, Paragraph
pair, Paragraph
using a set, Paragraph
subgroup, Paragraph
sum principle, Paragraph Paragraph Paragraph
for multisets, Paragraph Quotation
surjection, Problem Problem
number of, Problem
symmetric, Item
symmetric group, Problem Paragraph
transitive, Item
tree, Problem
spanning, Paragraph
spanning!cost of, Paragraph
spanning!minimum cost, Problem
Twentyfold Way, Paragraph
two row notation, Paragraph
type vector for a partition of an integer, Problem
type vector of a partition of a set, Problem
union of multisets, Paragraph
a structure using a set, Paragraph
degree of, Paragraph
of a complete graph, Paragraph Paragraph
walk, Paragraph
Young diagram, Paragraph