Your data matches 52 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
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',2]
 => 3 = 1 + 2
['B',2]
 => 5 = 3 + 2
['G',2]
 => 7 = 5 + 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: St001467
Mapping
St001467: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 4 = 1 + 3
['B',2]
 => 6 = 3 + 3
['G',2]
 => 8 = 5 + 3
Description
The number of involutions in the Weyl group of a given Cartan type. For type $A_n$, the generating function is $\exp(x+x^2/2)$, for type $BC_n$ it is $\exp(x^2+2x)$ and for type $D_n$ it is $\exp(x^2)(\exp(2x)+1)/2$.
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',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
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 5
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: 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',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
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 5
Description
The number of induced paths on three vertices in a graph.
Matching statistic: St001392
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St001392: 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]
 => 3
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 5
Description
The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.
Matching statistic: St001694
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001694: 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)
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 5
Description
The number of maximal dissociation sets in a graph.
Matching statistic: St000995
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000995: 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]
 => 2 = 1 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 4 = 3 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 6 = 5 + 1
Description
The largest even part of an integer partition.
Matching statistic: St000926
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000926: 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)
 => 4 = 1 + 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 6 = 3 + 3
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 8 = 5 + 3
Description
The clique-coclique number of a graph. This is the product of the size of a maximal clique [[St000097]] and the size of a maximal independent set [[St000093]].
Matching statistic: St000003
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St000003: 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]
 => [1,1,1]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [3,1]
 => 3
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [5,1]
 => 5
Description
The number of [[/StandardTableaux|standard Young tableaux]] of the partition.
Matching statistic: St000010
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
St000010: 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]
 => [3]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => 3
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 5
Description
The length of the partition.
The following 42 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000026The position of the first return of a Dyck path. St000147The largest part of an integer partition. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000668The least common multiple of the parts of the partition. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000708The product of the parts of an integer partition. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001128The exponens consonantiae of a partition. St001310The number of induced diamond graphs in a graph. St001389The number of partitions of the same length below the given integer partition. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001463The number of distinct columns in the nullspace of a graph. St001780The order of promotion on the set of standard tableaux of given shape. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000377The dinv defect of an integer partition. St000475The number of parts equal to 1 in a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000707The product of the factorials of the parts. St001073The number of nowhere zero 3-flows of a graph. St001176The size of a partition minus its first part. St001248Sum of the even parts of a partition. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001357The maximal degree of a regular spanning subgraph of a graph. St001480The number of simple summands of the module J^2/J^3. St001586The number of odd parts smaller than the largest even part in an integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000770The major index of an integer partition when read from bottom to top. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000146The Andrews-Garvan crank of a partition. St000474Dyson's crank of a partition. St000915The Ore degree of a graph. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra.