Your data matches 41 different statistics following compositions of up to 3 maps.
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Matching statistic: St001150
Mapping
St001150: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 2 = 1 + 1
['A',2]
 => 3 = 2 + 1
['B',2]
 => 4 = 3 + 1
['G',2]
 => 7 = 6 + 1
Description
The minimal dimension of a faithful linear representation of the Lie algebra of given type.
Matching statistic: St001128
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St001128: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 6
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 3
Description
The exponens consonantiae of a partition. This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].
Matching statistic: St000531
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St000531: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [3]
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,2,1,1]
 => 6
Description
The leading coefficient of the rook polynomial of an integer partition. Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
Matching statistic: St000757
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000757: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1] => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1,1] => 6
Description
The length of the longest weakly inreasing subsequence of parts of an integer composition.
Matching statistic: St000765
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000765: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1] => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1,1] => 6
Description
The number of weak records in an integer composition. A weak record is an element $a_i$ such that $a_i \geq a_j$ for all $j < i$.
Matching statistic: St000904
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000904: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1] => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1,1] => 6
Description
The maximal number of repetitions of an integer composition.
Matching statistic: St001235
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St001235: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1] => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1,1] => 6
Description
The global dimension of the corresponding Comp-Nakayama algebra. We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".
Matching statistic: St001236
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St001236: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => [1] => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [1,1,1,1,1,1] => 6
Description
The dominant dimension of the corresponding Comp-Nakayama algebra.
Matching statistic: St001659
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St001659: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [3]
 => 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,2,1,1]
 => 6
Description
The number of ways to place as many non-attacking rooks as possible on a Ferrers board.
Matching statistic: St001707
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St001707: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(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)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 6
Description
The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. Such a partition always exists because of a construction due to Dudek and Pralat [1] and independently Pokrovskiy [2].
The following 31 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001725The harmonious chromatic number of a graph. St000537The cutwidth of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001120The length of a longest path in a graph. St001777The number of weak descents in an integer composition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000479The Ramsey number of a graph. St000741The Colin de Verdière graph invariant. St001330The hat guessing number of a graph. St001345The Hamming dimension of a graph. St001391The disjunction number of a graph. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001642The Prague dimension of a graph. St001783The number of odd automorphisms of a graph. St001917The order of toric promotion on the set of labellings of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000454The largest eigenvalue of a graph if it is integral. St000939The number of characters of the symmetric group whose value on the partition is positive. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001621The number of atoms of a lattice. St001638The book thickness of a graph. St001644The dimension of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001742The difference of the maximal and the minimal degree in a graph. St001812The biclique partition number of a graph. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition.