Your data matches 16 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
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',1]
 => ([],1)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 6
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 8
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 10
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',1]
 => ([],1)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 6
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 8
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 10
Description
The number of facets in the chain polytope of the poset.
Matching statistic: St000301
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000301: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 8
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 10
Description
The number of facets of the stable set polytope of a graph. The stable set polytope of a graph $G$ is the convex hull of the characteristic vectors of stable (or independent) sets of vertices of $G$ inside $\mathbb{R}^{V(G)}$.
Matching statistic: St000915
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000915: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 8
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 10
Description
The Ore degree of a graph. This is the maximal Ore degree of an edge, which is the sum of the degrees of its two endpoints.
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',1]
 => ([],1)
 => [1]
 => 10 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 1010 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 10010 => 5 = 6 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 1000010 => 7 = 8 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 101010 => 9 = 10 - 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 $\binom{n}{a}_q$.
Matching statistic: St000391
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => 10 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 1010 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 10010 => 5 = 6 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 1000010 => 7 = 8 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 101010 => 9 = 10 - 1
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St000867
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000867: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [2,1]
 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => 5 = 6 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 7 = 8 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,2,1]
 => 9 = 10 - 1
Description
The sum of the hook lengths in the first row of an integer partition. For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below plus one. This statistic is the sum of the hook lengths of the first row of a partition. Put differently, for a partition of size $n$ with first parth $\lambda_1$, this is $\binom{\lambda_1}{2} + n$.
Matching statistic: St001228
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001228: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1,0]
 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,0,1,1,0,0]
 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 5 = 6 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 7 = 8 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => 9 = 10 - 1
Description
The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St000643
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000643: Posets ⟶ ℤResult quality: 80% ●values known / values provided: 80%●distinct values known / distinct values provided: 80%
Values
['A',1]
 => ([],1)
 => ? = 2 - 2
['A',2]
 => ([(0,2),(1,2)],3)
 => 3 = 5 - 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 4 = 6 - 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 6 = 8 - 2
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 8 = 10 - 2
Description
The size of the largest orbit of antichains under Panyushev complementation.
Matching statistic: St000228
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000228: Integer partitions ⟶ ℤResult quality: 80% ●values known / values provided: 80%●distinct values known / distinct values provided: 80%
Values
['A',1]
 => ([],1)
 => [2]
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 6
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 8
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => ? = 10
Description
The size of a partition. This statistic is the constant statistic of the level sets.
The following 6 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000770The major index of an integer partition when read from bottom to top. St000548The number of different non-empty partial sums of an integer partition. St000081The number of edges of a graph. St000941The number of characters of the symmetric group whose value on the partition is even. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001649The length of a longest trail in a graph.