Your data matches 69 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001747
Mapping
St001747: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 0
['A',2]
 => 1
['B',2]
 => 3
Description
The number of zeros in the character table of the Weyl group of a Cartan type.
Matching statistic: St001678
Mapping
St001678: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 1 = 0 + 1
['A',2]
 => 2 = 1 + 1
['B',2]
 => 4 = 3 + 1
Description
The symmetric bilinear form applied to the highest root and the Weyl vector of a finite Cartan type. The Weyl vector is half the sum of the positive roots, or the sum of the fundamental weights.
Matching statistic: St000107
Mapping
St000107: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 2 = 0 + 2
['A',2]
 => 3 = 1 + 2
['B',2]
 => 5 = 3 + 2
Description
The dimension of the representation $V(\Lambda_1)$. The sizes of $E_6$ and $E_7$ can be seen in [1].
Matching statistic: St000856
Mapping
St000856: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 2 = 0 + 2
['A',2]
 => 3 = 1 + 2
['B',2]
 => 5 = 3 + 2
Description
The number of conjugacy classes in the Weyl group of a finite Cartan type.
Matching statistic: St001370
Mapping
St001370: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 2 = 0 + 2
['A',2]
 => 3 = 1 + 2
['B',2]
 => 5 = 3 + 2
Description
The degree of the largest fundamental representation associated with a Cartan type.
Matching statistic: St000206
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000206: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 3
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. Given $\lambda$ count how many ''integer compositions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex. See also [[St000205]]. Each value in this statistic is greater than or equal to corresponding value in [[St000205]].
Matching statistic: St000448
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000448: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
Description
The number of pairs of vertices of a graph with distance 2. This is the coefficient of the quadratic term of the Wiener polynomial.
Matching statistic: St000940
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000940: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 3
Description
The number of characters of the symmetric group whose value on the partition is zero. The maximal value for any given size is recorded in [2].
Matching statistic: St000941
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000941: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 3
Description
The number of characters of the symmetric group whose value on the partition is even.
Matching statistic: St001308
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001308: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
Description
The number of induced paths on three vertices in a graph.
The following 59 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001347The number of pairs of vertices of a graph having the same neighbourhood. St001350Half of the Albertson index of a graph. St001521Half the total irregularity of a graph. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000244The cardinality of the automorphism group of a graph. St000321The number of integer partitions of n that are dominated by an integer partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001679The number of subsets of a lattice whose meet is the bottom element. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000009The charge of a standard tableau. St000016The number of attacking pairs of a standard tableau. St000081The number of edges of a graph. St000185The weighted size of a partition. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000348The non-inversion sum of a binary word. St000537The cutwidth of a graph. St001117The game chromatic index of a graph. St001161The major index north count of a Dyck path. St001310The number of induced diamond graphs in a graph. St001341The number of edges in the center of a graph. St001649The length of a longest trail in a graph. St001764The number of non-convex subsets of vertices in a graph. St001783The number of odd automorphisms of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001827The number of two-component spanning forests of a graph. St001961The sum of the greatest common divisors of all pairs of parts. St000086The number of subgraphs. St000184The size of the centralizer of any permutation of given cycle type. St000346The number of coarsenings of a partition. St000377The dinv defect of an integer partition. St000468The Hosoya index of a graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000644The number of graphs with given frequency partition. St001112The 3-weak dynamic number of a graph. St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001486The number of corners of the ribbon associated with an integer composition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001616The number of neutral elements in a lattice. St001754The number of tolerances of a finite lattice. St001757The number of orbits of toric promotion on a graph. St001815The number of order preserving surjections from a poset to a total order. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000395The sum of the heights of the peaks of a Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices.