Your data matches 28 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001964
(load all 2 compositions to match this statistic)
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',1]
 => ([],1)
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => 0
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 2
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: St001307
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001307: 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)
 => 0
['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)
 => 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)
 => 2
Description
The number of induced stars on four vertices in a graph.
Matching statistic: St001320
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001320: 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)
 => 0
['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)
 => 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)
 => 2
Description
The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. A graph is a disjoint union of paths if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.
Matching statistic: St001578
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001578: 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)
 => 0
['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)
 => 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)
 => 2
Description
The minimal number of edges to add or remove to make a graph a line graph.
Matching statistic: St000142
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',1]
 => ([],1)
 => [2]
 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => 3 = 2 + 1
Description
The number of even parts of a partition.
Matching statistic: St001092
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St001092: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [8,4,2]
 => 3 = 2 + 1
Description
The number of distinct even parts of a partition. See Section 3.3.1 of [1].
Matching statistic: St001214
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St001214: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 0
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,1,1]
 => 0
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [3,1]
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [5,1]
 => 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,1,1,1]
 => 2
Description
The aft of an integer partition. The aft is the size of the partition minus the length of the first row or column, whichever is larger. See also [[St000784]].
Matching statistic: St000533
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
St000533: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,1,1]
 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [3,1]
 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [5,1]
 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [3,1,1,1]
 => 3 = 2 + 1
Description
The minimum of the number of parts and the size of the first part of an integer partition. This is also an upper bound on the maximal number of non-attacking rooks that can be placed on the Ferrers board.
Matching statistic: St001415
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St001415: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => 1 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 01 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 11 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 11 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 101 => 3 = 2 + 1
Description
The length of the longest palindromic prefix of a binary word.
Matching statistic: St001416
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St001416: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => 1 => 1 = 0 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 01 => 1 = 0 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 11 => 2 = 1 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 11 => 2 = 1 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 101 => 3 = 2 + 1
Description
The length of a longest palindromic factor of a binary word. A factor of a word is a sequence of consecutive letters. This statistic records the maximal length of a palindromic factor.
The following 18 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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. St000256The number of parts from which one can substract 2 and still get an integer partition. St000480The number of lower covers of a partition in dominance order. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000940The number of characters of the symmetric group whose value on the partition is zero. St000257The number of distinct parts of a partition that occur at least twice. St000481The number of upper covers of a partition in dominance order. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001881The number of factors of a lattice as a Cartesian product of lattices. St001118The acyclic chromatic index of a graph. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001624The breadth of a lattice. St001783The number of odd automorphisms of a graph.