Index

Index

• G-set
• k-fold transitive
• k-graph
• k-graph, labelled
• k-subset
• r-cycle
• d -function, Kronecker's
• achiral object
• action
• adapted basis
• alphabet
• ambivalent
• automorphism, inner
• base, of an action
• Bell number
• bilateral class
• binomial function
• block
• block of a set partition
• cap operation
• cartesian product of groups
• Cauchy-Frobenius Lemma
• center of group
• center, of group
• chirality
• class function
• compatible subgroup
• complementary graphs
• complementary labelled graphs
• complete monomial group
• complete monomial group
• composition of groups
• convolution product
• cup operation
• cycle
• cycleproduct
• cycleproduct, associated
• de Bruijn's Lemma
• Dedekind number
• derangement number
• derivative of species
• diagonal subgroup
• digraph
• direct sum of groups
• disjoint cycles
• Dixon Wilf Lemma
• double coset
• edge of graph
• enantiomeric pair
• enantiomerism
• even permutation
• exponentiation group
• exterior cycle index
• Fermat's Congruence
• finite action
• fixed point
• Frobenius isomorphism
• Garsia-Milne bijection
• generating function
• graph
• graph, complementary
• graph, selfcomplementary
• graph, labelled
• graph, labelled simple
• group
• homogeneous component
• Homomorphism Principle
• imprimitivity system
• Inclusion and Exclusion, Principle of
• injective symmetry class
• interval in a poset
• invariant
• involution
• Involution Principle
• involution, sign reversing
• isomerism
• isomorphic labelled graphs
• labelled k-graph
• labelled graph
• labelled graph, complementary
• list notation
• locally finite poset
• loop, of graph
• Lyndon's Theorm
• mark
• minimality test
• Moebius function
• Moebius-matrix, of group
• molecular graphs
• multiplicative weight
• necklace problem
• normal basis
• normalizer
• odd permutation
• orbit
• ordered set partition
• part, of a partition
• plethysm of groups
• pointwise stabilizer
• poset
• power group
• primitive orbit
• principle, Inclusion Exclusion
• principle, Two Involutions
• proper partition
• punctuation of species
• Pólya substitution
• Pólya's Theorem
• Redfield's Lemma
• regular representation
• relabeling
• rencontre number
• rooted tree
• Rothe diagram
• second kind, Stirling numbers of
• selfcomplementary graph
• selfenantiomeric orbit
• set partition
• setwise stabilizer
• sieve-equivalent
• sign reversing involution
• sign function, on set
• signless Stirling number of the first kind
• similar actions
• Sims chain
• species
• Stirling number second kind
• Stirling's Formula
• stratum
• subaction
• superposition, of graphs
• Surjective Resolution
• surjective symmetry class
• symmetric
• symmetry adapted basis
• test, for minimality
• transport of structure
• transposition
• tree
• Two Involutions' Principle
• type of element
• vertex of graph
• weak Bruhat order
• word
• wreath product
• zeta function
• zeta-matrix, of a group
• A-structures connected
• A-structures labelled
• q-binomial number
• q-binomial theorem
• actions homomorhic
• actions inner isomorphic
• actions isomorphic
• actions similar
• action character of
• action faithful
• action finite
• action natural
• action restriction of
• action transitive
• algebra incidence
• associated species
• basis adapted
• basis normal
• basis symmetry adapted
• Bruhat order weak
• Burnside Lemma
• Burnside matrix
• Cauchy-Frobenius Lemma weighted form
• centralizer of element
• centralizer of subset
• character of action
• class bilateral
• component connected
• component homogeneous
• conjugacy class of group element
• conjugacy class of subgroup
• connected A-structures
• connected components
• connected graphs
• connected graph
• content critical, orbit
• content of a mapping
• coset double
• coset left
• coset right
• Coxeter group
• cycle indicators plethysm of
• cycle index
• cycle index exterior
• cycle indicator
• decomposition theorem, Redfield's
• faithful action
• filter principal
• function binomial
• function incidence
• function Kronecker's d
• generalized wreath product
• graphs connected
• graphs superposition of
• graph connected
• graph molecular
• group Coxeter
• homomorphic actions
• incidence algebra
• incidence function
• inner automorphism
• inner isomorphic actions
• Involution Principle weighted form
• isomorphic actions
• Kronecker d-function
• labelled A-structure
• left coset
• left regular representation
• lemma Burnside's
• lemma Cauchy-Frobenius'
• lemma Cauchy-Frobenius' weighted form
• lemma de Bruijn's
• lemma Dixon and Wilf's
• lemma Redfield's
• length of base
• length of word
• Lyndon decomposition
• Lyndon length
• Lyndon set
• Lyndon words
• Moebius function number theoretic
• Moebius Inversion Theorem
• natural action
• normalizer of subset
• number theoretic Moebius function
• number q-binomial
• number Dedekind
• operation cap
• operation cup
• orbit content critical
• orbit primitive
• orbit type of
• order ideal, principal
• partition of a set
• permutation even
• permutation odd
• permutation representation
• plethysm of cycle indicators
• pointwise stabilizer
• point fixed
• poset locally finite
• principal filter
• principal order ideal
• principle homomorphism
• Redfield's Theorem Counting
• Redfield's Theorem Decomposition
• reduced sequence
• representation left regular
• representation permutation
• representation regular
• restriction of action
• right coset
• sequence reduced
• setwise stabilizer
• sign of permutation
• species associated
• species derivative of
• species punctuated
• stabilizer pointwise
• stabilizer pointwise
• stabilizer setwise
• stabilizer setwise
• structure labelled
• structure transport of
• structure type of
• subgroup conjugacy class of
• subgroup normalizer of
• Sylow Theorem
• system of imprimitivity
• tabloid truncated
• theorem q-binomial
• theorem Lyndon's
• theorem of Moebius Inversion
• theorem Pólya's
• theorem Redfield's Counting Theorem
• theorem Redfield's Decomposition
• theorem Sylow's
• transitive action
• truncated tabloid
• type of an orbit
• type of structure
• weight function
• weight multiplicative
• wreath product generalized

Index