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# IndexIndex

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