Your data matches 31 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001635
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St001635: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => -1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 1
Description
The trace of the square of the Coxeter matrix of the incidence algebra of a poset.
Matching statistic: St000181
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = -1
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St000261
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000261: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
['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)
 => ? = -1
Description
The edge connectivity of a graph. This is the minimum number of edges that has to be removed to make the graph disconnected.
Matching statistic: St000262
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000262: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
['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)
 => ? = -1
Description
The vertex connectivity of a graph. For non-complete graphs, this is the minimum number of vertices that has to be removed to make the graph disconnected.
Matching statistic: St000287
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000287: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
['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)
 => ? = -1
Description
The number of connected components of a graph.
Matching statistic: St000310
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000310: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
['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)
 => ? = -1
Description
The minimal degree of a vertex of a graph.
Matching statistic: St001000
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => [1]
 => [1,0,1,0]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [1,0,1,0,1,0]
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => ? = -1
Description
Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001487
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001487: Skew partitions ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => [1]
 => [[1],[]]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [[2,1],[]]
 => 1
['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
Description
The number of inner corners of a skew partition.
Matching statistic: St001490
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001490: Skew partitions ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => [1]
 => [[1],[]]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [[2,1],[]]
 => 1
['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
Description
The number of connected components of a skew partition.
Matching statistic: St001518
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001518: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 75%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
['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)
 => ? = -1
Description
The number of graphs with the same ordinary spectrum as the given graph.
The following 21 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001625The Möbius invariant of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001722The number of minimal chains with small intervals between a binary word and the top element. St001765The number of connected components of the friends and strangers graph. St001820The size of the image of the pop stack sorting operator. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000286The number of connected components of the complement of a graph. St000311The number of vertices of odd degree in a graph. St000315The number of isolated vertices of a graph. St000322The skewness of a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001577The minimal number of edges to add or remove to make a graph a cograph. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001871The number of triconnected components of a graph. St000770The major index of an integer partition when read from bottom to top.