Processing math: 85%

Your data matches 55 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001945
Mapping
St001945: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 4 = 3 + 1
['B',2]
 => 5 = 4 + 1
['G',2]
 => 7 = 6 + 1
['A',3]
 => 9 = 8 + 1
Description
The number of non-isomorphic subgroups of the Weyl group of a finite Cartan type. This statistic returns the number of non-isomorphic abstract groups. See [[St001155]] for the number of conjugacy classes of subgroups.
Matching statistic: St000643
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000643: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 4
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 6
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 8
Description
The size of the largest orbit of antichains under Panyushev complementation.
Matching statistic: St000104
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000104: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 5 = 3 + 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 6 = 4 + 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 8 = 6 + 2
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 10 = 8 + 2
Description
The number of facets in the order polytope of this poset.
Matching statistic: St000151
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000151: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 5 = 3 + 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 6 = 4 + 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 8 = 6 + 2
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 10 = 8 + 2
Description
The number of facets in the chain polytope of the poset.
Matching statistic: St000147
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000147: 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]
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 4
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 6
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => 8
Description
The largest part of an integer partition.
Matching statistic: St000770
(load all 4 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000770: 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]
 => 4 = 3 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 5 = 4 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 7 = 6 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 9 = 8 + 1
Description
The major index of an integer partition when read from bottom to top. This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top. For example, the partition λ=(8,6,6,4,3,3) has corners at positions 3,6,9, and 13, giving a major index of 31.
Matching statistic: St001908
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St001908: 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]
 => 2 = 3 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 3 = 4 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 5 = 6 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 7 = 8 - 1
Description
The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. For example, there are eight tableaux of shape [3,2,1] with maximal entry 3, but two of them have the same weight.
Matching statistic: St000010
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ 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)
 => [3,2]
 => [2,2,1]
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [2,2,1,1]
 => 4
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => [2,2,1,1,1,1]
 => 6
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => [3,3,2,2,1,1,1,1]
 => 8
Description
The length of the partition.
Matching statistic: St000081
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St000081: 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)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 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)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 5 = 6 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 7 = 8 - 1
Description
The number of edges of a graph.
Matching statistic: St000290
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000290: Binary words ⟶ 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]
 => 1010 => 4 = 3 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 10010 => 5 = 4 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 1000010 => 7 = 6 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 101010 => 9 = 8 + 1
Description
The major index of a binary word. This is the sum of the positions of descents, i.e., a one followed by a zero. For words of length n with a zeros, the generating function for the major index is the q-binomial coefficient \binom{n}{a}_q.
The following 45 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000391The sum of the positions of the ones in a binary word. St000867The sum of the hook lengths in the first row of an integer partition. St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000057The Shynar inversion number of a standard tableau. St000148The number of odd parts of a partition. St000301The number of facets of the stable set polytope of a graph. St000309The number of vertices with even degree. St000915The Ore degree of a graph. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001459The number of zero columns in the nullspace of a graph. St000941The number of characters of the symmetric group whose value on the partition is even. St000384The maximal part of the shifted composition of an integer partition. St000474Dyson's crank of a partition. St000784The maximum of the length and the largest part of the integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000145The Dyson rank of a partition. St000225Difference between largest and smallest parts in a partition. St000228The size of a partition. St000517The Kreweras number of an integer partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in an integer partition. St000479The Ramsey number of a graph. St001917The order of toric promotion on the set of labellings of a graph. St000459The hook length of the base cell of a partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St001725The harmonious chromatic number of a graph. St000160The multiplicity of the smallest part of a partition. St000475The number of parts equal to 1 in a partition. St000548The number of different non-empty partial sums of an integer partition. St001091The number of parts in an integer partition whose next smaller part has the same size. St001644The dimension of a graph. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St001127The sum of the squares of the parts of a partition.