# 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

action of a group on a set, Paragraph

arithmetic progression, Problem

arithmetic series, Problem

associative law, Problem

asymptotic combinatorics, Paragraph

basis (for polynomials), Paragraph

Bell Number, Problem

bijection principle, Paragraph

binomial coefficient, Paragraph

\(q\)-binomial, Problem

Binomial Theorem, Problem

extended, Problem

broken permutation, Paragraph

Burnside's Lemma, Paragraph

Cartesian product, Paragraph

generating function for, Problem

Catalan Path, Problem

Cauchy-Frobenius-Burnside Theorem, Paragraph

characteristic function, Problem

chromatic polynomial of a graph, Paragraph

Chung-Feller Theorem, Problem

closure property, Item

coefficient

multinomial, Problem

coloring

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

\(k\) parts, Exercise

number of, Exercise

composition of functions, Problem

compositions

number of, Exercise

congruence modulo \(n\), Problem

conjugate of an integer partition, Problem

connected component graph, Problem

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

definition

inductive, Paragraph

recursive, Paragraph

degree of a vertex, Paragraph

ordered, Exercise

deletion, Paragraph

derangement, Paragraph

derangement problem, Paragraph

diagram

of a partition!Ferrers, Paragraph

of a partition!Young, Paragraph

dihedral group, Subsection

Dijkstra's algorithm, Problem

disjoint, Problem

multisets, Paragraph

distance in a graph, Problem

distance in a weighted graph, Paragraph

domain (of a function), Paragraph

strong, Paragraph

driving function, Paragraph

Dyck path, Problem

in a digraph, Paragraph

of a complete graph, Paragraph

EGF, Paragraph

encomplement of a partition, Problem

enumerator

fixed point, Problem

orbit, Problem

equivalence class, Paragraph

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

Ferrers diagram, Paragraph

fix, Paragraph

fixed point enumerator, Problem

alternate definition, Paragraph

bijection, Paragraph

characteristic, Problem

composition, Paragraph

digraph of, Paragraph

driving, Paragraph

identity, Paragraph

injection, Problem

inverse, Paragraph

onto!and Stirling Numbers, Problem

ordered, Paragraph

ordered!onto, Paragraph

relation of, Paragraph

functions

composition of, Problem

number of, Theorem

one-to-one!number of, Theorem

onto!number of, Problem

generating function, Paragraph

exponential, Paragraph

exponential!product principle for, Paragraph

ordinary, Paragraph

product principle for, Problem

geometric progression, Paragraph

graph, Paragraph

chromatic polynomial of, Paragraph

coloring of, Paragraph

coloring of!proper, Paragraph

complete, Paragraph

coordinate, Paragraph

distance in, Paragraph

simple, Paragraph

graphs

isomorphic, Problem

Gray Code, Exercise

greedy method, Paragraph

group acting on a set, Paragraph

group action on colorings, Paragraph

group of permutations, Paragraph

identity property, Item

identity property (for permutations), Paragraph

inclusion and exclusion principle, Paragraph

for unions of sets, Paragraph

indicator polynomials, Paragraph

induction

mathematical, the strong principle of, Quotation

strong double, Paragraph

inductive

conclusion, Paragraph

hypothesis, Paragraph

step, Paragraph

inductive definition, Paragraph

inverse function, Paragraph

inverse property, Item

involution, Problem

isometry, Problem

isomorphic

graphs, Problem

k-set structures, Paragraph

Lah number, Paragraph

lattice path, Problem

diagonal, Problem

length (of a path), Paragraph

constant coefficient, Paragraph

homogeneous, Paragraph

second order, Problem

mathematical induction

strong double, Paragraph

method

probabilistic, Paragraph

minimum cost spanning tree, Problem

monochromatic subgraph, Problem

multinomial coefficient, Problem

multiorbit, Paragraph

multiorbits, Problem

multiplicity in a multiset, Problem

multiset, Problem

multisets

product principle, Paragraph

quotient principle, Paragraph

sum principle, Quotation

union, Paragraph

ménage problem, Problem

one-to-one, Problem

one-to-one function, Problem

counting, Problem

ordered, Paragraph

onto functions

number of, Problem

orbit, Paragraph

orbit enumerator, Problem

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

partition

blocks of, 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

path

in graph, Problem

lattice, Problem

lattice!diagonal, Problem

length of, Paragraph

permutation

\(k\)-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

principle

bijection, Paragraph

product!general, Paragraph

quotient, Paragraph

principle of inclusion and exclusion, Paragraph

for unions of sets, Paragraph

probabilistic method, Paragraph

product

Cartesian, Paragraph

product notation, Paragraph

for multisets, Paragraph

picture enumerators, Problem

product principle for exponential generating functions, Paragraph

product principle for generating functions, Problem

progression

arithmetic, Problem

geometric, Paragraph

proper coloring of a graph, Paragraph

Pólya-Redfield Theorem, Problem

range (of a function), Paragraph

recurrence, Paragraph

deletion-contraction, Problem

linear homogeneous, Paragraph

solution to, Paragraph

two variable, Paragraph

recurrence relation, Paragraph

recursive definition, Paragraph

reflexive, Item

relation, Paragraph

of a function, Paragraph

recurrence, Paragraph

transitive, Item

rising factorial power, Paragraph

rotation group, Paragraph

second order recurrence, Problem

self-conjugate partition, Problem

sequence

degree, Exercise

series

arithmetic, Problem

set

colorings of action of a group on, Subsection

sets

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

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

surjections

number of, Problem

symmetric, Item

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

walk, Paragraph

Young diagram, Paragraph