Your data matches 207 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000854
Mapping
St000854: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 1
['B',2]
 => 2
['G',2]
 => 2
Description
The number of orbits of reflections of a finite Cartan type. Let $W$ be the Weyl group of a Cartan type. The reflections in $W$ are closed under conjugation, and this statistic counts the number of conjugacy classes of $W$ that are reflections. It is well-known that there are either one or two such conjugacy classes.
Matching statistic: St000860
Mapping
St000860: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 1
['B',2]
 => 2
['G',2]
 => 2
Description
The size of the center of the Weyl group of a finite Cartan type.
Matching statistic: St001158
Mapping
St001158: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 1
['B',2]
 => 2
['G',2]
 => 2
Description
The size of the mutation class of quivers of given type.
Matching statistic: St001950
Mapping
St001950: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 1
['B',2]
 => 2
['G',2]
 => 2
Description
The minimal size of a base for the Weyl group of the Cartan type. A base of a permutation group is a set $B$ such that the pointwise stabilizer of $B$ is trivial. For example, a base of the symmetric group on $n$ letters must contain all but one letter. Any base has at least $\log |G|/n$ elements, where $n$ is the degree of the group, i.e., the size of its domain.
Matching statistic: St001700
Mapping
St001700: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 1 + 2
['B',2]
 => 4 = 2 + 2
['G',2]
 => 4 = 2 + 2
Description
The maximum degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.
Matching statistic: St001964
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 0 = 1 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 1 = 2 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 1 = 2 - 1
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St000142
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000142: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2
Description
The number of even parts of a partition.
Matching statistic: St000148
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000148: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 2
Description
The number of odd parts of a partition.
Matching statistic: St000256
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000256: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2
Description
The number of parts from which one can substract 2 and still get an integer partition.
Matching statistic: St000286
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000286: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 1
Description
The number of connected components of the complement of a graph. The complement of a graph is the graph on the same vertex set with complementary edges.
The following 197 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000480The number of lower covers of a partition in dominance order. St000482The (zero)-forcing number of a graph. St000537The cutwidth of a graph. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000776The maximal multiplicity of an eigenvalue in a graph. St000778The metric dimension of a graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001092The number of distinct even parts of a partition. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001270The bandwidth of a graph. St001281The normalized isoperimetric number of a graph. St001323The independence gap of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001644The dimension of a graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001742The difference of the maximal and the minimal degree in a graph. St001961The sum of the greatest common divisors of all pairs of parts. St001962The proper pathwidth of a graph. St000171The degree of the graph. St000271The chromatic index of a graph. St000312The number of leaves in a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000618The number of self-evacuating tableaux of given shape. St000636The hull number of a graph. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000928The sum of the coefficients of the character polynomial of an integer partition. St001057The Grundy value of the game of creating an independent set in a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001307The number of induced stars on four vertices in a graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001354The number of series nodes in the modular decomposition of a graph. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001366The maximal multiplicity of a degree of a vertex of a graph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001638The book thickness of a graph. St001642The Prague dimension of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001883The mutual visibility number of a graph. St001110The 3-dynamic chromatic number of a graph. St001345The Hamming dimension of a graph. St001383The BG-rank of an integer partition. St001625The Möbius invariant of a lattice. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St000378The diagonal inversion number of an integer partition. St000159The number of distinct parts of the integer partition. St000160The multiplicity of the smallest part of a partition. St000257The number of distinct parts of a partition that occur at least twice. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000287The number of connected components of a graph. St000288The number of ones in a binary word. St000309The number of vertices with even degree. St000363The number of minimal vertex covers of a graph. St000392The length of the longest run of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000481The number of upper covers of a partition in dominance order. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000553The number of blocks of a graph. St000627The exponent of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000753The Grundy value for the game of Kayles on a binary word. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000783The side length of the largest staircase partition fitting into a partition. St000897The number of different multiplicities of parts of an integer partition. St000916The packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000982The length of the longest constant subword. St000992The alternating sum of the parts of an integer partition. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001128The exponens consonantiae of a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001267The length of the Lyndon factorization of the binary word. St001282The number of graphs with the same chromatic polynomial. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001342The number of vertices in the center of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001368The number of vertices of maximal degree in a graph. St001372The length of a longest cyclic run of ones of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001432The order dimension of the partition. St001437The flex of a binary word. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001463The number of distinct columns in the nullspace of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001568The smallest positive integer that does not appear twice in the partition. St001716The 1-improper chromatic number of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001884The number of borders of a binary word. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St000052The number of valleys of a Dyck path not on the x-axis. St000143The largest repeated part of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000225Difference between largest and smallest parts in a partition. St000274The number of perfect matchings of a graph. St000295The length of the border of a binary word. St000313The number of degree 2 vertices of a graph. St000315The number of isolated vertices of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000386The number of factors DDU in a Dyck path. St000391The sum of the positions of the ones in a binary word. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000547The number of even non-empty partial sums of an integer partition. St000552The number of cut vertices of a graph. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000659The number of rises of length at least 2 of a Dyck path. St000676The number of odd rises of a Dyck path. St000792The Grundy value for the game of ruler on a binary word. St000934The 2-degree of an integer partition. St000935The number of ordered refinements of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000940The number of characters of the symmetric group whose value on the partition is zero. St000944The 3-degree of an integer partition. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001172The number of 1-rises at odd height of a Dyck path. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001214The aft of an integer partition. St001252Half the sum of the even parts of a partition. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001286The annihilation number of a graph. St001315The dissociation number of a graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001335The cardinality of a minimal cycle-isolating set of a graph. St001341The number of edges in the center of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001363The Euler characteristic of a graph according to Knill. St001389The number of partitions of the same length below the given integer partition. St001413Half the length of the longest even length palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001484The number of singletons of an integer partition. St001512The minimum rank of a graph. St001524The degree of symmetry of a binary word. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001587Half of the largest even part of an integer partition. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001657The number of twos in an integer partition. St001689The number of celebrities in a graph. St001691The number of kings in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001730The number of times the path corresponding to a binary word crosses the base line. St001783The number of odd automorphisms of a graph. St001910The height of the middle non-run of a Dyck path. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001930The weak major index of a binary word. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000299The number of nonisomorphic vertex-induced subtrees. St000351The determinant of the adjacency matrix of a graph. St000452The number of distinct eigenvalues of a graph. St000847The number of standard Young tableaux whose descent set is the binary word. St000997The even-odd crank of an integer partition. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path.